Think of meter as a poem's underlying structure—the rhythm beneath the words in each line. Does the poem go daDUM daDUM daDUM? Does it go dadaDUM? How about daDUMda daDUMda? Answer that question and you've got the poem's meter.
Of course describing a poem in daDUMs can only get you so far. At some point you're going to run out of noises and need some vocabulary.
First, you should know that meters are composed of feet. The type of foot being used, and the number of times that foot is repeated in each line, will give you the name of the meter you're reading. So, for example, if the foot is an iamb (daDUM), and it's repeated five times, you're dealing with iambic pentameter.
There are, of course, a ton of different kind of feet, so knowing those terms will help you on your way to becoming a metrical master. For now, we'll just list 'em: iamb, trochee, spondee, anapest, dactyl, amphibrach, and pyrrhic.
Those terms, of course, only cover the first half of what we call meter. The second half comes from the number of times that foot is repeated. If it's monometer, the foot is only used once. Dimeter repeats the foot twice. Trimeter three times, tetrameter four times, pentameter five times, and hexameter six. We could go on (guess how many times heptameter and octameter repeat their feet?), but we won't, because we have a feeling you get the picture. Plus, as you study poetry, you're probably going to spend most of your time reading trimeter, tetrameter, pentameter, and hexameter.
Once you've got the basic vocab down, you're ready to start analyzing meter. Figuring out that a poem is written in iambic pentameter or, say, trochaic tetrameter is just the first step on the long, wonderful road of metrical analysis, a.k.a. scansion.
See, a poet may choose to write in anapestic trimeter, sure, but if the whole stinkin' poem were in that meter, it would get a little boring after a while. So poets like to add what we call metrical variation into the mix. Is there an iamb thrown smack dab into the middle of a line of anapests? Does a line of iambic pentameter start with a trochee? And what's the effect of that change? These, Shmoopers, are the questions that metrical analysis asks.
Think of metrical analysis as yet another way to open up and think about a poem (as if you needed more ways to open up a poem). Good writing is about much more than the words on the page; it's about how they sound, and how that sound contributes to meaning. So understanding meter can be yet one more tool in your reading arsenal. Use it well, Shmoopers. Use it well.