Pumps are categorised by their Horse Power (HP), although they are often badged with a Kilowatt rating (KW, see below). Swimming pool pump manufacturers develop a model and then sell it in, usually, 4 Horse power sizes. So for example the company Sta-Rite have, among other things, their Dyna-Glas pump and it comes in 0.5, 0.75, 1.0 and 1.5 Horse Power.
The important thing for the pool owner is not so much the Horse Power but the amount of water the swimming pool pump can move in an hour. The amount of water it can move depends upon how much resistance the pipes etc. put upon it. The resistance of the pipes etc. is measured in "metres of head". It is possible to work out the resistance in your pool pipework but it is very complicated. Most domestic pools have a resistance of 10 to 13 metres. As a rule of thumb, you should circulate your entire pool volume in 8 hours, so your hourly capacity should be the volume of your pool divided by 8.
So, for a 15ft x 30ft pool at an average of 5 ft deep, our volume calculator (in the help section) tells us the volume is 64 cubic metres. Divide 64 by 8 and you get 8m3 per hour required. If this was your pool you would need to choose a pump with a capacity greater than 8m3 per hour. In most cases you will see a 0.75 Horse Power pump is what you need.
When you look at the plate on your pump it often quotes the power in KW. To convert KW to HP (approximately) multipy by 1.33. Here is a table for the common swimming pool pumps.