Arissa is a woman fleeing from Orion Syndicate assassins, and that takes her to Deep Space Nine. Odo's personal interest in her protection soon becomes a personal interest in her, and the two begin a romance. But Arissa has a secret unknown even to her, and alien assassins won't stop coming for her until she's dead.
This episode was inspired by a 1952 movie called The Narrow Margin, which show runner Ira Steven Behr says many TV series have cribbed. (It involves a cop protecting a witness that he doesn't know is also a cop posing as a decoy to deflect attention from a real witness.) Behr also commented that Deep Space Nine never really did romance very well; discounting the long-term ones (Sisko and Kasidy Yates, Dax and Worf), he's probably right. But at least this romance has a reason to come and go all in the span of one hour of television.
It's nice to give Odo some dating experience here, before getting him into a relationship with Kira later in the series -- though perhaps that wasn't the plan. (Rene Auberjonois in fact thought at the time that this episode was moving Odo and Kira apart for good.) Odo needs that experience, because he's simply not equipped for a relationship. He has to go to his friends for advice -- a pretty big exposure of his normally bottled-up feelings. Those friends are warmly supportive. Kira and Bashir both tell Odo to go for it. Sisko and Dax expressly state how happy they are to see him happy.
What doesn't come up (because no one was really thinking about such things in the 1990s) is the extreme power imbalance in this scenario. The alien Arissa is a woman on the run -- quite capable, but in a truly desperate situation. She's fleeing a form of prostitution, which the episode is a bit coded about, but which seems to involve letting men intrude into her data-port-modded mind for money. Odo has offered to help her, but then makes advances on her. She is really not in a position where she can refuse, unless she's willing to risk losing his help. Thankfully, at the end of the episode, once Arissa's true memories are restored, she makes clear that her alter ego really did love Odo, removing the quite unfortunate possibility that she was acting against her true wishes.
Assuming that rather dark interpretation of the story doesn't cross your mind, what we do see is the life cycle of a fairly sweet relationship. Arissa impresses Odo at first by how she handles Quark -- and indeed she handles Odo in the same moment, flustering him by commenting on his "bedroom eyes." Their relationship grows in a way unique to them: it's built on lying to each other at first (a lot!), but with each knowing the other is doing it. In very clever but subtle camera work by director John Kretchmer, the two are rarely shown together in a single shot until their "morning after" in bed -- and that shot is a gently floating, minutes-long, uninterrupted take.
The romance can't last more than a single episode for a reason that makes sense: Arissa isn't who she thinks she is. She has a husband she didn't know about. (It would have been fun if the daughter she'd pretended to have early in the episode turned out to be real, too.) In a way, Rene Auberjonois has a greater acting challenge in not being able to cry to show his emotion. Odo physically can't shed tears, but Auberjonois makes his sadness and sense of loss clear to us all the same.
What doesn't work so well is the threat to Odo and Arissa's relationship. The Orion Syndicate is a menacing mafia in the abstract, but Star Trek hasn't put in the work to show us much of it by this point in the franchise. And the Syndicate's representatives in this episode are a cliche "smart one / dumb one" pairing that are played for comic relief at least as much as for peril.
The episode didn't really need that comic relief either, as it gets enough from the tiny subplot about another "Julian Bashir, Secret Agent" holo-adventure. After the the events of "Our Man Bashir," Julian's friends are now playing spy with him for fun. (And after legal threats from MGM, it's kept largely off-screen, and is not so explicitly a parody of James Bond.) It's especially fun to see O'Brien complain about having to be the bad guy again, then throwing into the role with relish all the same -- and tossing off a casual "hi Odo" as he gets the drop on Julian.
Other observations:
- Kira mentions how "perceptive" Arissa is to note Odo's bedroom eyes. This is ironically an unperceptive moment for her, in that she's never picked up on any of the clues to Odo's interest in her.
- Arissa later proves not as perceptive as advertised, when she fails to recognize the purpose of Odo's "furniture," something Lwaxana Troi picked up on immediately.
- Worf gets grouchy when everyone gossips about Odo's relationship. Oh, so now Worf disapproves of sticking your nose into other people's romantic business? (Maybe he's learned a lesson?)
- In his first draft script, writer Rene Echevarria reportedly included a scene visiting a holographic night-club singer -- very much the character who would later become Vic Fontaine. It was cut here in part for length and in part because they'd hoped to cast either Frank Sinatra Jr. or Steve Lawrence, but couldn't get either.