Ok- lemme try to help.
Many devices, such as keyboards, electronic drums, etc., use a digital language known as MIDI. This stands for Musical Instrument Digital Interface. MIDI is basically a way for devices to "talk" to each other.
When you strike an electronic drum pad it sends MIDI messages to the "sound module" of the device (aka the brain). The brain contains all of the actual "sounds" you hear, which could be anything - a cowbell, a snare, a dog barking, etc. or even a combination of sounds. Other messages include how loud to play that sound, for how long, etc.
So when you strike the pad, you are merely "triggering" the brain to play something from it's memory bank. Are you with me so far?
Many keyboards and drum machines contain sequencers. More often, a computer will handle this task. A sequencer is "basically" a device for recording, editing, storing and playing back these MIDI messages.
A huge benefit of using MIDI is in the editing capabilites. Let's say you record a drum beat using snare, kick and hihat. When you listen back you notice you're timing is way off. You can easily edit (fix) this in the sequencer, either by moving the notes where you want them or using "quantize", which aligns all the beats to a grid defined by the user. You can also easily change any of the sounds, say you decide you wanted the hihat to be a ride cymbal instead, etc.
Lemme know if this helps you understand triggers and sequencing better.
You also might be interested to know that there are several software packages that have tons of beats and drum machines built in. -Rez
