Backing a horse or team on Betfair means placing a bet which will payout to you if the horse or team wins the race or match. If the horse loses then you lose your stake.

For instance, if you Back £10 @ 3.50 on the Favourite horse in the race, that means you want the Favourite to win:

If Horse wins:
Back bet wins so you will be paid £10 x 3.50 = £35 (including your original stake)

If Horse loses:
Back bet loses so you will lose your £10 stake.

Every bet that is matched on Betfair has at least 2 counterparties: the Layer and the Backer. A bet is matched when both the Layer and Backer agree on a price.