It means that it can switch up to a total of 15 amps. I'm assuming you are referring to an AC controller by the way. Even if you are running 16 150W 240V ropelights that only maxes out at 2400W or 10 amps. Most people are actually moving away from 240V AC lights here in aussie in favour of low voltage (typically 24V) DC lights as they are safer and the controllers are cheaper and easier to come by.
With the low voltage power supplies they general output say 24v at 15amps max, but the input is quite allot lower something like that would only draw 2 - 2.5amps tops. So you would be safe to run one or two off a normal 10amp power point