A sequencer (in music, not genetic splicing,) is a kind of recorder, that records what your fingers do (through a keyboard plugged in to the sequencer, via MIDI* usually), and then lets you record more instruments in harmony with the first performance, and even correct, or change the speed or key of what you did, after you've finished performing it.
The way it works, is to divide each musical beat into a large number of very small 'ticks' or 'clock pulses'. For example, each beat of a 1-2-3-4- piece of music, might be divided by the sequencer, into 480 tiny little ticks. At each tick, the sequencer looks at what the keys on the keyboard are doing, and makes a record of which keys are going down, (and how fast they are pressed-louder or softer) which keys are going up, and which keys are just being held down, whether the sustain (foot) pedal is being pressed, etc.  Then, when you stop "recording" and "rewind" and press "play" (just like a cassette recorder,) the sequencer plays back everything you've just done, as accurately as it's teeny little computer-brain can.
You can then change the channel, and record a whole new part, to go with the first part. Or go after it. You could first record a piano part, on Channel 1, then stop, go to Channel 2, and record a violin section to go with the piano. (You would have to set your synthesizer to Piano on Channel 1, and Violin Section on Channel 2.)

Well, that's it in a nutshell.
*For more info, you could visit the Internation Committee for MIDI Standards
but this guy here seems to be more to the point: guy who is more to the point
Or we could return to what we were just doing.........

   In my work, I use the LinnSequencer, a 14 year old piece of equipment, designed by Roger Linn, an inventor generally accepted as the father of Drum Machines. Its software is updated by the Forat Brothers. They are cool Rocket Scientists and Dance Mixers, who work in the Valley (LA.)
    If the piece is quite complicated, or if I want to record real 'live' sound WITH the sequence, I use Digital Performer on my Macintosh computer. It's a really great program developed by Mark of the Unicorn, in Cambridge, Massachusetts.