'Meter' refers to the rhythm of the poem, created by the pattern of stressed and unstressed syllables. An iamb is simply an unstressed syllable followed by a stressed one. A trochee, on the other hand, is a stressed syllable followed by an unstressed one.
It's sometimes useful to think about meter in terms of music: a stressed syllable would be on the beat, whilst an unstressed syllable would be off beat. Iambic meter, then, ends up sounding like da-DUM da-DUM da-DUM (think of the Pink Panther theme tune), whilst trochaic meter is the opposite, DUM-da DUM-da DUM-da.
A lot of Renaissance poets and play-writes used iambic meter, such as Shakespeare's 'to BE or NOT to BE'. It mimics the usual rhythm of natural speech so is well suited to monologues, and tends to sound quite soft and rhythmic. Trochaic meter, on the other hand, sounds a lot more forceful: think of William Blake's 'TYGer TYGer BURNing BRIGHT'. The trochaic meter here gives a thumping effect reminiscent of the tiger's footprints and the heart and hammer imagery later in the poem.
If you're having trouble identifying the meter of a poem, try saying the words aloud as you would in a normal conversation; be careful not to force the words to fit the meter you want. If you try to say the line aloud using iambic or trochaic meter, it is usually quite obvious when it doesn't fit. For example 'TO be OR not TO be' would not sound right, and neither would 'tyGER tyGER burNING bright'. An easy way to note down the meter of a poem is to write a small 'v' above unstressed syllables and a '/' above stressed ones. Once you have done this you can see from the patterns that emerge whether it is iambic (v/v/v/), trochaic (/v/v/v), or neither.
Of course, not all poems fit either of these meters, but checking the meter of an unseen poem can be a good 'way in' to analysis. It is also often worth commenting on any moments in a poem that break from the meter of the rest, as this is very rarely accidental: think about what makes that point different to the rest of the poem and what effect the break from the meter has. A sudden change in meter may emphasise a certain word, or signify a turning point, and often creates a sense of discomfort and disorder.