What is a three verse poem?

A stanza of three lines is sometimes called a tercet, sometimes a triplet. There is no consistency of usage to distinguish between the two terms (though many sources will claim there is: frequently contradicting each other).

The specialised three line stanza which is used for narrative chains by riming

ABA BCB CDC DED ....

Is called terza rima. Terza rima is the metre of Dante's Divine Comedy, and a specialised form of it appears in Shelley's Ode to the West Wind.