The poem is about the poet's inability to handle liquor. In other words, she gets drunk easily. After three drinks, she is so drunk that instead of sitting at the table, she is now under the table. After four drinks, she might sleep with her host.

One martini is okay Two martinis is the most I can drink without behaving improperly Three martinis make me drunk enough that I fall on the floor and end up under the table Four martinis make me drunk enough that I am (or want to be) having sex with the host of the party

If you're "under the table", you are very drunk. Under your host... well, think about that one. :)