The Seagull on its title page proposes to be a "comedy in four acts," but only the last three words seem to be accurate. The plot involves an neurotic aspiring artist Constantine, his actress mother, and some assorted romantic entanglements. I agree with the introduction that Chekov's plays are not without plot, but I'd say the plot really doesn't matter much because you can rapidly surmise the romances won't come to much and ultimately the outcome isn't very important.
I thought this play was a bit less interesting than Ivanov, but very similar in the sense that its characters are equally obsessed with their own misery. Constantine in particular emphasizes his incompetence. Even the most upbeat character in the play, the writer Trigorin, emphasizes that his life will be summed up on his tombstone as "not as good as Turganev." Probably the most interesting aspect of the play is associated with its title: the seagull which Treplev kills for his love Nina. Nina (and I) don't make much sense of this supposed symbol from Treplev's perspective, but Trigorin later runs with it and uses it to represent a woman after she meets a man who "wrecks her life for want of anything better to do." In this case, it's reflective of the relationship that develops between Nina and Trigorin until the latter becomes bored.
Constantine, presumable speaking for Chekov, pontificates at length (perhaps too much length!) about the nature of writing, the theater and the need for Russian authors to move beyond their current rut. He mentions the addition of dreamlike elements on the stage, but this seems like it couldn't be further from the direction Chekov heads in his later plays. I already read those a year or two ago but I'll probably read them again...maybe not this time around though.