Earned at least $x$ total score for at least $y$ answers in the $z$ tag.
How can I know how much have I constituted in any tag, and also where can I find the description of these badges.
Go to the "Tags" section of your profile.
Put your cursor over each number to see your activity within that tag.
All badge descriptions are available on the tab that says "Badges" at the top of the site: