Take the following scenario:
You own a company that is profitable (and therefore has to pay Corporation Tax on any profits, as well as Income Tax/NI on payments/drawings). You (and your mates, also employed by your company) attend football each week, have a few beers and a bite to eat before each game (let's say it costs you £60 each, per week).
If your company sponsors something at football it's effectively a way of transferring a benefit from your company, to yourself (and your mates), and has three advantages:
1. You and your buddies all (presumably) get wined and dined before the game, and/or get seats included in the sponsorship package.
2. It's classed as employee entertaining, so is (should be?) tax deductible.
3. You and your mates all get to keep the £60 (per week) that you would have otherwise spent.
(and of course, that's not to mention putting money into the club and hopefully gaining some business from the sponsorship).