What is the benefit of getting a certain number of upvotes on comments? The tooltip says it means that the comment is "useful", but how is someone rewarded for posting useful comments?
There is a Pundit badge, which is silver and awarded for ten comments with five upvotes or more each.
Other than that, there is no reward. This is by design - comments are "second-class citizens." We want to focus on the questions and answers here, not the comments.
Quoting the FAQ post :
When there are many comments on a post, some comments are hidden when the page loads, and there is a button to “show N more comments”. The comments with the fewest upvotes are hidden first. The threshold depends on the number of comments on the post and on the number of answers on the page.
When there are a lot of comments, any important information in them tends to get lost. To minimize loss of any important or useful information, comment upvotes come into play.
No reputation of any kind is earned or lost from comment votes, though the Commentator badge is is awarded for leaving 10 comments, and the Pundit badge is awarded to those who left 10 comments with score of 5 or more.
Comments are however, by design, second class citizens, which is why there is no rep to gain for writing good comments. Ideally, any or all useful information should be available within the post body.
Then why the badges?
Bronze badges generally exist to motivate users to familiarize themselves with the system and how it works. Comments are an important part of the system, even more so on meta sites.
The silver badge exists to promote good behavior, that is, correct usage of the comment feature. Its there to motivate users to write useful comments and not contribute to the noise.