Don't ask about it, because it will disqualify you in a dealers eyes (if he knows what he's doing), and if a dealer would say it as his opening statement... well, you know what you've encountered....
The wattage on speakers means only one thing: "How much abuse will be required before they start burning?" Unless you're a DJ or will arrange outdoor concerts, you'll never need to know about it.
There... that's done...
So... is the wattage interesting at all? Yes - in the amplifier. In most cases, more wattage doesn't mean you will be able to play louder; most amplifiers can play loud enough. More wattage means it won't "sweat" as hard, so a stronger amplifier (might) sound better at the same volume. (No flames, please - I'm painting with a broad brush and I'm aware of it)
So, how many watts are enough then? Well, it depends on your loudspeakers.
There are two things you need to know about your speakers and are what you
should ask about in the store (instead of the wattage ;-): sensitivity and impedance.
Sensitivity is the measurement of how much volume you will get from your speaker
given a certain amount of "watts" into it. The "normal" is 90 dB (decibell).
If it's less, you need more amplifier power, if it's higher you need less. If the
difference is +- 1 or 2, it doesn't matter so much... And if it's higher, it's not
a problem, but it can be an indication of a loudspeaker only built to play loud...
_Most_ high quality speakers are below 92dB. If it's 87 or below, you will probably
need a little more powerful amplifier...
Impedance indicates how (electrically) demanding it is on the amplifier. Normal is 8 ohms. If it's 4, the amplifier needs to give out twice the power... The power of the amplifier is given over 8 ohms, and very few amplifiers gives twice as much when you give then 4 ohms... 2 is very problematic.
And the combination must be regarded... Low sensitivity + low impedance = a difficult speaker. In some newspapers, there are something called a "power cube measurement" that shows how an amplifier operates when encountering different loads (= different speakers). It should be as close to a box as possible. The more it looks like a skislope, the more of a "problem" it will have with low impedance speakers.
Could you follow me here? Well... that's about all you need to know... There's lot of other technical terms and measurements, but none are really important in the beginning. If you're on a Holy Grail crusade for the ultimate sound, you'll have read papers & talked to enough people to have gotten the rest of the terms nailed down.