Brute force attacks have two possible rewards for the attacker: gain access to the site back end by correctly guessing the password *or* take down the targeted site/server for a period of time by causing a Denial Of Service.

Of these results, the most dangerous is gaining access to the site's back end as from that point the attacker can do whatever they want to your WordPress installation. A Denial of Service just means your site is unreachable or offline for a period of time (although if a server is misconfigured, this too can become dangerous and allow attackers to access more than they should).

So to address this you really need two solutions: 1) Use a unique and hard to guess password to reduce the likelihood of a successful guess by an attacker (two factor authentication helps a lot here) and 2) make it hard for attackers to even access the login functionality to try and attack it (HTTP Basic Authentication helps here).