Why the minimum load?

I just replaced the power converter in a lighting fixture with 5 20W 12V halogen lights.

I had been thinking I'd replace the halogens with CFLs or maybe LEDs, but the power converter (PDF data sheet) indicates it has a minimum load of 50W. Lower power lights would likely take me below this limit. This converter takes standard 120VAC/60Hz and produces 11.8V at 30kHz.

I don't know how this kind of converter works, so I'm hoping someone could explain why there's a minimum load. If I go below it, will it just not turn on?

Depends. It might just go out of regulation and give a different voltage, or have oscillations, or who knows what. My guess would be higher output voltage than spec, just looking at the load curve. Hook up a power resistor and see what it does (or just one halogen bulb @ 20W).

Many switching power supplies require a minimum load.

For a fixed frequency, pulse width modulated, switching power supply, as the load get lighter the duty cycle gets shorter. Below about 5%, things get dicy for the stabilty of the feedback control voltage regulation.

Many new supplies allow pulse skipping to keep the duty cycle above a minimum level. This can give a bit more ripple in the supply voltage however.

The different voltage could be as high as the supply voltage, and the oscillations could cause circuits to have complex and destructive AC interactions. Speakerguy pretty much said it all.