The harness will "basically" hardwire your headlights directly to the battery in effect bypassing the stock wiring that is already in your car. The relay will act as the on-off switch for the power to get from the battery to the lights. The relat is controlled by the stock headlamp switch, so instead of turning on the lights directly, you turn on the relay, which turns on the headlights.
Because the harness will allow you to draw power directly from the battery instead of drawing power thru the 12+ year old stock wiring in your car, this will allow more juice to flow to the light and not "get lost" along the way. More juice means mo-better light output from the bulb. The headlamp housing itself will still be a limitting factor since it is also 12+ years old and may be dirty, pitted, scratched, discolored, moldy, contaiminated, etc...