Here's how I explain it to people.
Think of ohms as resistance. The more resistance you have, the less power (like swimming in water is 2ohms of resistance, but swimming in honey would be 8ohms of resistance). Speakers have a set resistance on each voice coil (where you hook the speaker up, or the + and - terminals for simplicities sake sale it the voice coil). So when a speaker is a single voice coil 4ohm speaker, if you hook it up to an amp that puts out 200watts @ 4 ohms, it will obviously put out 200w. Now if you have a 2ohm sub and that amp does not go down to 2ohms stable, you will be pulling more power out of the amp than it's designed for. It will get hotter and probably go into protect mode.
What can start to get confusing is when you have multiple voice coils (whether on the same or different speakers themselves). You have two ways of hooking them up , either series or parallel (or combination)
http://www.eng.cam.ac.uk/DesignOffice/mdp/electric_web/DC/DC_7.html
That's a general link about series and parallel. The main importance to remember is that parallel decreases resistance (measured in ohms) and series add to resistance. The matt is really easy. two 4ohm voice coils, can be bridged in parallel (remember lowers resistance) so the final ohms of resistance would be 2ohm (or final impedance). If we wired them inseries, it would double to 8ohms. Either way it can double or halve (assuming same voice coil impedances)
seriesl
parallel
The real important thing to note here is series is only making one pathway through the voice coils so it hits 4ohms of resistance then another 4ohms on each voice coil, adding up to 8ohms total resistance
parallel on the other hand splits the connection, therefore making multiple paths for the power to through different voice coils. Its like adding multiple lanes on a highway, the more lanes you have the more traffic, so you would halve that number down to 2. The more "lanes" like in my analogy, the less resistance, the less resistance the more power.
http://mobile.jlaudio.com/support_pages.php?page_id=161 Good link showing visual representations of all the ways to wire up subs.
Remember, don't run an amp below its lowest rated impedance. Most 2 ch amps are rated 2ohm stereo, and 4ohms bridged. So two 4ohn voice coils could only be hooked up at 8ohms bridging that amp (remember it would halve if we wired it in parallel to 2ohms, below that minimum impedance or resistance).