Headlights use a relay because you really don't want to have to route the thicker wires required to handle the current used by headlights all the way from the fusebox to the switch and then back to the headlights. Instead, even old cars run a thin "hot" wire to the switch and then to a relay that handles the higher current for the lights. Both the switch wire and the wire after the relay may be fused, so you need to check for more than one blown fuse.
More modern/expensive cars will run that wire from the headlight switch to an integrated headlight module which has all the switches and relays necessary to run every light in the car. It's great for manufacturing simplicity but it means that when it quits working, instead of opening a fusebox and replacing a relay you might have to swap out a $1000 lighting module instead.
If you have the car service manual, you should run through the diagnostic tree since that should point you to exactly what fuses and stuff to check. If you don't have the service manual, you have the choice of either paying $100 for the manual, or paying some service tech $100 to troubleshoot the problem. Either way, you're gonna pay so you might as well buy the service manual and do the work yourself.
