Iconic: Captain Orzik and Lieutenant Sylas
The Black Talon is the Imperial equivalent of the The Esseles: the optional flashpoint you encounter just after you've finished your starter planet and are about to move on to Dromund Kaas. Both were tacticals before tactical flashpoints were even a thing, and somewhat surprisingly they've undergone nearly no changes with 4.0 - unlike all the other flashpoints, these are still limited to levels 10-15 on the group finder, probably because Bioware was keenly aware of how strongly their stories are tied to you being low-level and new. This means that you get scaled to level 10 instead of up to 65 when you enter. They did however also add a solo mode version for both factions' flashpoints that you can do whenever you like. I tried the one for the Black Talon and having a GSI droid by my side felt like complete overkill, considering that these flashpoints were already easily soloable for a skilled player before 4.0.
Like the Esseles, the Black Talon is all about the story.
Shortly after you've boarded the Black Talon to travel to Dromund Kaas, you're greeted by the ship's second in command, Lieutenant Sylas, who points out that "your" droid is waiting for you with a message in the nearby conference room. You go to investigate and meet NR-02, an innocent enough looking protocol droid, who soon identifies himself as being programmed for much more unpleasant tasks. (I'm sure I wasn't the only one who had to look up "calumniation" in the dictionary.) He gets you in touch with Grand Moff Kilran, who wants the Black Talon to intercept the Republic ship Brentaal Star and kill or capture an Imperial traitor on it who is only known as "the General" throughout the entire story. The Black Talon is uniquely positioned to achieve this, but its captain has refused to obey Kilran's orders, which is why the Moff wants you to usurp command and get the job done yourself.
You have to fight your way to the bridge and kill some Imperials on the way. Captain Orzik puts up a brave face as you arrive and threaten him, justifying his decision by saying that what Kilran demands is simply impossible. You have the option to merely relieve him of command or kill him.
Having assumed command one way or the other, you chase down and engage the Brentaal Star, and it spits out some pods in defense. If you let Orzik live, he'll identify them as a threat and have them shot down, which leads to you being boarded by a regular boarding party instead. Once you defeat the Republic boarders, Orzik presents you with a small chest of extra goodies which he had his crew put together, since you're all working together now after all.
If you killed Orzik however, the much less experienced Lieutenant Sylas, now effectively Captain, will tell the crew to ignore the pods, causing the ship to get swarmed by a bunch of sabotage droids. You then have to go and fight those off instead.
Once you've repelled the attack, you fly over to board the Brentaal Star and fight your way inside to kill or capture the general, dispatching of a Mon Calamari war veteran and a Jedi padawan in the process. Eventually you find the General, who is a squat, elderly cyborg and already wounded. He babbles about what terrible plans both factions have already made to prepare for war, a dialogue which is fun to come back to as a max level player as you actually know what he's talking about by then. You have the option of taking him prisoner or outright killing him. Then you return to the Black Talon.
"I had nothing to do with any of this, honest!"
If you left Captain Orzik alive, everything is well and everyone is pleased. If you killed him however, the crew has panicked in your absence and ended up shooting each other, so that the bridge is littered with nothing but corpses. Or that's what NR-02 says happened anyway... considering his earlier declaration of being programmed for manslaughter and calumniation, you may have to take that with a grain of salt. Grand Moff Kilran is happy either way and you can either continue to Dromund Kaas or return to the fleet. (NR-02 assures you that he can pilot the ship even with everyone else dead.)
You fight mostly Republic soliders and droids, but also some Imperial ones, when you take over the ship at the start. The lesson here is that the Empire does not value the lives of its subjects very highly. NR-02 even comments: "If you are concerned about the loss of life, I assure you - the deaths of all injured crew members will be strategically insignificant."
Like on the Esseles, the boss encounters are all very basic and geared towards players who are new to the game, though I think the ones on the Black Talon are less interesting overall than their Republic counterparts. (I admit that my Republic bias might be playing into this however.) Only Commander Ghulil, the Mon Cal war veteran, is really worth noting because he teaches players not to stand in fire (quite literally, as he drops probes that spit fire).
Like the Esseles with its encounter with Sith apprentice Vokk, the Black Talon tries to make a big deal out of you meeting (what's supposed to be) your first Jedi in the form of Yadira Ban, even if she's only a padawan, but she just doesn't come across as very threatening - maybe because she's a pink twi'lek with a squeaky voice? She has one noteworthy ability where she pulls you in and then does some damage if you don't run away from her quickly enough, but it's only really dangerous on hardmode.
Yadira Ban - just not that threatening.
Speaking of hardmode, while I haven't run the Black Talon on hard since 4.0, it's interesting to note that at level 50 it used to be known for having by far the easiest hardmode of all flashpoints, to the point where you didn't even need a full group to do it. This is an interesting contrast to its Republic equivalent, which originally had one of the hardest of all hardmodes.
I could write a lot of the same stuff here that I said about the Esseles: that it's an amazing narrative experience the first time but can get tedious when you have to re-run it for endgame rewards. However, instead I'd like to focus on the differences between the Black Talon and the Esseles.
Both serve to introduce you to your faction's storyline in a way, and they really highlight the differences between the two factions. While both flashpoints are about a small ship getting into big trouble, their stories are almost complete opposites in other ways. Where the Esseles is operating in pure self-defense, trying to fight off an Imperial attack, the Black Talon is on the offense, hunting down a traitor. On Republic side the main characters of your faction that you interact with are a shrewd diplomat, a somewhat cowardly officer and a fearless security chief. On Imperial side on the other hand you deal with a ruthless droid, a bloodthirsty Moff and an Imperial crew who desperately want to do the right thing but are incredibly frightened by the power plays going on, which is really a pretty good summary of what Imperial life is like! The only thing missing is a capricious Sith bossing everyone around, but effectively the player gets the chance to play that role if they choose to play a Sith character.
It's also worth noting that in terms of narrative and gameplay, the Black Talon has far fewer twists and turns than the Esseles, but manages to make your choices feel quite a bit more meaningful. The singular choice of whether you let Captain Orzik live or not decides not only which boss encounter you will face at the start (either the boarders or the lead sabotage droid) but also the fate of the entire Black Talon's crew. Whether to kill or spare the captain was actually a part of Bioware's early marketing for the game, supposed to highlight the importance of choices. They even gave out badges after demos where people got to try out the Black Talon so they could announce their choice to the world - too bad that kind of thing didn't carry over into more content.