As poem titles go, this one is pretty on-the-nose: "Spring" is a poem about spring and all things spring-y. But we should keep in mind that the poem is actually a song sung at the end of a play within a play. In the play, the song is basically untitled. So, this title is really no more than a marker used when the song is published separately from the play itself.
Still, using this generic title does have an effect on how we experience the poem. When we see the word "spring," we think of all the bright sunny things typically associated with spring. Spring is a word brimming with positive associations. So even before we begin to read the poem we have expectations of what it will hold. What we get certainly fulfills some of these expectations (blooming flowers, singing birds), but the negative reaction of the married men to the cuckoo's song takes us a bit by surprise. The poem is, in a sense, contemplating the negative aspects of spring amid all that positivity and beauty.