I'd like to add some thoughts to what andrew has said. Actually it's not easy to find good definitions of what these terms mean. Andrew defines poems as fruit of poetical inspiration. So poems are defined by "poetical" which explaines not much. Or as "skilled art", but which skill or art comes into play remaines open. Also this definition would be true only when talking about good poems because unskilled art produces bad poems, but poems nonetheless. So why not call them poems?
Poetry then is defined as a collection of poems, therefore it's defined by the term "poem" which we found ill defined before. So there seem to be some problems in defining absolutely what these terms refer to.
What ethne's question aimed at, their relation to each other, is somewhat easier to find. Still it's not that simple either. Poetry sometimes is used in the way andrew explains it, as a collection or totallity of poems. For example when you say that Goethe's poems are a part of German poetry of the 18. and 19. century. But what about sentences like: "I like poetry"? By stating this, you wouldn't necessarily mean that you like every poem that was ever written, or even that you like the whole of poems. You're rather saying that you like a certain genre of text production which can be differentiated from other genres like novel, tragedy, newspaper article or advertisement which can be characterised more or less by certain language features or certain ends they are produced for or a certain usage and meaning in life. From this perspective it's not poetry which is defined by poems but the other way round: poems are single instances of poetry, single language products fitting into the genre features that are specific to poetry.
I'd like to add that to my knowledge poesy can also mean the art of producing poetry. So a poet's poetry can mean all of his/her poems or his/her special style in making poems whereas his/her poesy would refer to his/her skill in doing that. A book on poesy would not