Basically, it is advertising, it depends on your location and typical advertising format. With the prevalence of social media these days, we use it as part of the promotional platform. The best example I can think of is NHRA drag racing (because I love it). Every card is plastered with sponsors stickers and logos. We have banners we reuse every year, but we also have a graphics shop make up smaller sponsor banners to go alongside.
We promote our tournaments locally in online and in print and include the major sponsors.
Beyond that, we don't 'offer' much. More for fun, some of the sponsors have done some promotional spots during the tourneys.
In reciprocity, circuit tournament competitors wear gear from manufacturers sponsors.