When looking at guitar amplifiers you will see these words quite a lot, especially if you are hunting for a stack amp. This is because these affect what speakers will work with your current amplifier. If you buy a mismatched head and cab it can cause serious damage to both pieces of kit.
Wattage is the power rating of your amplifier. This is how much it can push out of the speaker at maximum volume. Do not get it confused with a volume rating as power does not correlate directly. Some 15w amps can be much louder than other 30w amps. It all comes down to the design and how it was built (valve, solid state etc.). This means as long as cabinet wattage > amp wattage you are fine.
The Impedance is an interesting thing but all you need to know is that your head and cab need to match. For example if you cab has an 8 ohm input make sure you use the mono 8 ohm output on your head. If you are using multiple cabinets it can get a little complicated and changes on an amp by amp basis.
For example you may buy an amplifier with an 8ohm output at 100w but your cabinet may have a 8ohm input and can only handle 60w. At bedroom volume you may not cause much damage but once you turn up something will go wrong.
That is why it is important to always buy a cab that matches impedance (ohms) and can handle at least what your amplifier is rated at in terms of wattage. Normally with 4×12 cabs this is not much of an issue as most speakers are rated high enough to handle most heads when split over 4 speakers. When using a single or dual speaker setup though you do have to be extra careful that you do not damage anything.
If you are not sure always try and find the matching cab that was meant to go with your head. Not only will it often deliver the best sound but it will also run extremely safely as well.