A poem is written by composing lines of metrical feet (those are like beats or counts of syllables), arranged rhythmically. If you're looking to impress your crush, try penning a poem.
Poetry is literature in metrical form, and a poem is what we call a piece of poetry. There are so many different kinds of poems it's almost impossible to define, but usually poems are written in short lines, and sometimes don't have too many lines. What counts in a poem is distilling something down, and finding the right words. If someone tells you that your Tweets are like little poems, then you must be a lovely writer.