I noticed that there is a "Badges Plugin" at the left column when i visit a user's profile. Is this a plugin i can download and use also in my forum ?
Welcome to the community.
The badges plugin used on here is proprietary.
There is an open source reactions application called YAGA.
The original developer no longer seems to be updating it, but another user has forked it to work with Vanilla 2.5 +
See here: https://open.vanillaforums.com/discussion/comment/251690/#Comment_251690