Welcome to Meta Stack Exchange, which is a separate site in the network with its own reputation system, functioning exactly like a main site like Stack Overflow (though privilege levels might be a bit different). So just like on Stack Overflow, downvoting answers costs reputation.
On per-site Metas like Meta Stack Overflow, you cannot lose (or earn) reputation; that reputation is always synchronized from the account on the corresponding main site. The following section from the Stack Overflow Help Center is 'missing' from the one used here:
If you have an account on Stack Overflow, you have an account on its meta site.
You do not need to create a separate account for meta; once you are logged in on Stack Overflow, you are also logged in and may post on its meta site.
Votes on meta do not affect your reputation; your meta reputation is the same as your reputation on Stack Overflow (synchronized hourly), though you earn separate badges. You must have 5 reputation to participate on meta.