A MIDI sequencer is something like Cakewalk, Cubase, Logic, ProTools or something like that. The terminology dates back to when computers sent MIDI information to keyboards and drum machines and basically acted like "piano rolls" to play back songs. MIDI is the language that keyboards and synths use to govern note pitch, duration etc. Nowadays "sequencers" actually involve much more and can record, edit and playback audio as well as apply effects and run "soft synths" so called because they emulate external synths but are wholly contained within the sequencer. You may have heard of VST or DirectX "plugins" which are add-on effects or soft-synths. By the way "synths" here also includes drum machines and a whole host of other virtual instruments.
Garage band is essentially a sequencer. It handles audio clips and MIDI clips and allows you to compose, structure and edit tunes on the computer.
Now, the thing about triggering loops live is that you need to a) have something to trigger the MIDI note that launches the loop b) some kind of virtual sampler or software that will take that MIDI note and know what loop to trigger and possibly c) some way of making sure that the tempo of the loop is communicated back to the band (drummer?). I'll cover getting the sound from your computer to the PA in a moment.
So to address a) you can either use a mouse to "launch" the loop, or tap something on the computer keyboard, or play a note on an keyboard/synth (using a MIDI cable to connect the synth to your computer), or use some dedicated MIDI controller or floorboard (e.g. something by M-Audio / Evolution or a Behringer FCB1010 floorboard or something similar). Some MIDI controllers (keyboards) now link to the computer using USB, so having a special MIDI interface isn't really essential anymore, unless you've got some older gear already available.
To address b) you'll need to set up your sequencer to be able to translate the MIDI note to the relevant loop. You can use a plugin that acts as a virtual sampler to do this, or you might be able to tell garageband directly to do this (I'm sorry I'm not familiar with garageband). The thing is that you probably want to have several different loops available, so you want something that knows which loop to play when. You probably also want a setup that allows you to switch between loops without having to close a program or file and open another. That's why b) is important.
To address c) we need to talk about audio interfaces. Your computer will have a stereo output. That's good enough provided you don't want to have your drummer hear the metronome or click. That may be a bad idea. Correction, that *WILL* be a bad idea. Any time I've tried looping in a band situation things have gotten out of sync pretty quickly. So you need to have some way of running the loop to the PA through one output, and a metronome, click or monitor channel through another. You CAN split the stereo output of your computer so that the loop goes to the PA in mono (which usually isn't a problem) and run the other "half" of the signal to your drummer via some headphones. This involves having a Y cable. Male connection at one end and two females at the other. You can get these in some specialist PA and audio stores.
So after all of that, do you still want to go ahead and do it?
The idea of having loops running in a performance seems a fairly trivial task - hey, you've got a computer and some software that plays loops. NO PROBLEM! But the reality to get the system working in a foolproof way during a performance is quite another thing.
Good luck if you try going down this road. Let us know how you get on. Let me know if you need any further info...
All the best,
Mike