While there's a really technical explanation of Watt Seconds, in practical terms its a relative measure of how much flash a studio style flash will create. All flashes have a capacitor that power the flash tube - the capacitor is charged up slowly and then all the energy is released in a burst through the flash tube. Studio flashes generally have a power cord that runs to a wall outlet and use the watt second rating.
In my experience - 150 W/S isn't bad for a single person, 300 W/S is good for a small group, a couple of 300 W/S flashes is good for a group of about 10, a couple of 1000 W/S flashes(but ideally three or so flashes) is good for a group of 30 to 50, and 2400 W/S is good for doing product photography where you need a lot of Depth of Field when close focusing (which is going to be around f16 to f45. Or when you're doing larger products.
These are just rough usages for assorted flashes - as a rule, more is better. By using a higher power flash at a lower setting, you get a lot faster recharge rate (how quickly you can flash again) and more consistency - I find with flashes at full power I tend to shoot people too quickly and so the flash isn't back up to full power.
