"Poetry" is a hard word to define, but you usually know a poem when you see it. One reason you can easily recognize a poem is that usually (not always) poems are written in verse, which is the opposite of prose. The opposition is very simple, on the surface: Verse is language written in lines. (See Reference, verse and prose.)
Well, yes, prose is in lines too -- and if the prose isn't fully "justified" (in the printer's sense of the word), we can't even say that the right-hand margin of a piece of prose has to be a straight vertical line. But in verse, the breaks between lines mean something.
When you're reading prose, you don't imagine that the author expected you to pause at the end of every printed line and ask why it ended there. The author probably didn't even know where the printer (or the word-wrap control on a computer screen) would break the lines. When you're reading verse, though, you know that the author broke the lines deliberately; and it's a good guess that those deliberate choices participate in the meaning of the poem, like all the other choices an author makes.
One thing a line-break can mean is that the line has reached some predetermined length. Like two and a half inches? Well, no. Poetry is originally an auditory, not a visual art; and this question of length is one of many important consequences that follow from this fact. During most of the history of English poetry, the way the length of a line is measured has been metrical: a pattern -- usually consisting of some number of syllables, usually with some related pattern of stresses -- has been fulfilled.
That's still a visual, mechanical way of understanding meter: as a measure-rule that each line in the poem obeys. But usually the poet is especially concerned with the auditory effects of the pattern. After all, even when they're presented in the visual medium of print, poems are sounding words, meant to be heard, at least by your inner ear, if not actually passing through your vocal chords. Beginning from sound, we can build up a different definition of meter: as a way of controlling rhythm.
Any set of words (like any set of sounds) has some kind of rhythm. But poems, if we read them well, make us especially aware of the rhythm of the words, and arrange for it to be meaningful in some way. To make this happen, poets control or organize the rhythms of language into patterns. Meter is one kind of pattern, historically a very important kind.
Metrics is the study of methods that poets use to control the rhythm of language in poems. Why study them, the rhythm of a poem's language is audible to anyone who listens. But you've probably forgotten how you learned the complex, meaningful rhythms of English speech; if English is your native language, it was a long time ago. Poetic rhythms, too, demand some practice before you can hear them fully. And practice is most efficient if you understand what you're practicing. This is especially true of the patterns in metrical verse, because poets and readers have been collaboratively building up conventions, or habits, of writing and listening for several centuries.
This English Metrics hypertext can teach you all the main conventions (and the terminology that embodies the conventions) that you need in order to hear the poem's rhythms with full understanding. It does this mostly in the traditional way, by teaching you to scan the poem.
To understand what scansion is, let's go back a step. Meter is a more or less unvarying pattern applied to the always varying rhythms of a poem's individual lines. There's a relation between meter and rhythm similar to the relation between "the human face" (two eyes either side of the nose, mouth below that, ears outboard halfway up, and so on), and your face, which your friends don't confuse with anyone else's. Scansion is a way -- a crude but often useful way -- of characterizing an individual line of verse by drawing a diagram of its rhythm's relation to the meter that governs all similar lines.
From here, it's a short step to all the details, a little mystifying on first encounter, of "feet," "iambs," "caesurae," and the rest of the terminology you'll learn in English Metrics. These terms are analytical tools, developed over generations, to make it easier to talk about what happens when we hear the rhythms of poetic lines in relation to the meter underlying them.
If we were starting over from scratch, we might design different tools, and we would certainly give them different names. (The names we have are mostly Greek, which tells you how long this has been going on.) Some writers on prosody have tried to do that. But the traditional system has the advantage of any traditional system: a lot of people know it, and can use it to communicate with each other.
We can finish up by deducing, from the general principles outlined up to this point, two basic Rules.
Rule 1: You have to listen to the poem to read it. If you read it the way you read a newspaper, or a textbook you must get through before tomorrow morning, it won't mean much to you. Learning a little about metrics is useful simply because it will help you hear the poem better.
Rule 2: When you're reading verse, pay attention to where the lines end. Meter is one way lines get "measured," but free verse (which means "verse that isn't metrical") uses a variety of different principles. What all verse has in common is that the line is in some way a significant unit of language, like the word and the sentence.
Use the terms and methods of metrical study because they make learning to hear more efficient. They're just tools. The point is the poem. For the moment, just take on faith the odd fact that many people have found real fun in learning the system of English metrics.