Symbolism, Imagery, Allegory
Well, it's the title of the play so we guess it might be an important symbol. Nina likens herself to a seagull in Act 1, and the image recurs throughout the play. In the second act, Konstantin has shot a seagull to get Nina's attention. She sees his act as meaningless melodrama, but he threatens to kill himself with the same method—and eventually succeeds.
When Trigorin discovers the dead seagull, it triggers an idea for a story:
"A young girl… loves the lake the way a seagull does, and she's happy and free as a seagull. Then a man comes along, sees her, and ruins her life because he has nothing better to do. Destroys her like this seagull here." (2.117)
Rather than running as fast as possible in the other direction, Nina is excited about this potential self-sacrifice, and offers her life to Trigorin in Act 3. The seagull pops up again in Act 4. In a pretty tacky move, Trigorin had asked for it to be stuffed, a monument to his destruction of Nina. Now he's forgotten that it (and she) exist.
So what does the seagull mean? It's only beautiful when it's flying free, untouched by human involvement. Once it's used as a tool for love—once Konstantin shoots it and Trigorin stuffs it—that beauty gets twisted and soiled. The seagull image last appears in Nina's tearful, bothered speech in Act 4. She recognizes her own entrapment but won't free herself from love of the man who destroyed her.