You might have noticed that Yelena is hot stuff at the estate. Everyone's into her or jealous of her, but she is annoyingly faithful to old Serebryakov (we suspect that if Vanya hadn't walked in on Astrov kissing her, the story would be different, but, hey…). In one attempt to get her to loosen up, Vanya tells her that she's a mermaid:
VOYNITSKY: Why languish? [Animatedly] Well, my dear, splendid creature, do something clever! In your veins flows a mermaid's blood, so be a mermaid. For once in your life let yourself go, fall head over heels in love with some water sprite—and plop, head first, into a whirlpool, so the Herr Professor and all of us just raise our hands in amazement! (3.38-43)
Why would Vanya say something like that? What does a mermaid have to do with Yelena, a landlubber? Well, if you'll remember your mythology, the mermaids are sirens who use their singing to attract sailors to them but actually cause them to crash on the rocks.
That mix of seduction and danger is what Vanya is trying to describe when he calls Yelena a mermaid. And that gets to her. The problem isn't just that she doesn't want to let go with Vanya. She's got another sailor in mind, Astrov:
YELENA ANDREYEVNA: [...] Yes, I'm bored when he isn't around, I'm smiling now I'm thinking of him… That Uncle Vanya says I have a mermaid's blood in my veins. 'For once in your life let yourself go'… So? Perhaps I should… (3.122-25)
For the characters in Uncle Vanya, the mermaid is a symbol of bucking societal expectations and constraints, like Yelena's marriage to Serebryakov, for example, and just doing what feels good, "letting go" and diving in with Astrov or Vanya. They must be far from the sea, though, because no one is brave enough to actually dive in.