Purpose of power handling in the specs?

Maybe part tradition and part guidance. I have typically run speakers with twice the power their rating recommended. Not going for loud but impactful.

I think the guidance is to give a very uninformed consumer something to hang their hat on. So, as an uniformed consumer you buy a cheap $200 amp with 20 wpc and try to make these power guzzling towers sound good… they have given guidance that this was not going to turn out well.

Informed audio folks generally ignore most all of the published stuff… or at least look for anything odd… then look at efficiency and listen to what they sound like. I don;t think I payed attention to power handling in any speaker I have bought in 40 years at least.

You answered your own question. It's how much power the speakers can handle.

rated to handle between 50-200 watts of power

 Shocking isnt it. 

Yes, it is electricity after all.

@erik_squires   cool calculator thanks.  So my 96dB speakers that claim they can handle 600 watts input (I'm driving with less than a watt) will generate 124dB at one meter....

Indeed shocking.

Important to note that speaker makers are usually a little optimistic with their measurements, but they should be from anechoic (no echo) testing.  In room performance will vary, but the power to volume ratios (dB) will remain constant.  3dB more power = 3dB louder until compression sets in.