[3D models] Why calculate tangents?

So I’ve seen here and there tangents being used in 3D graphics. My question is, why? My first thought was that it may be something to do with lighting, because of how a tangent of a circle/plane is where a line touches, but not intersects it. So maybe it was used for not calculating light for a specific face behind another. Which could be done with basic shadow mapping… Then I thought it may have to do with shadow mapping… And now I’m just really confused…

I also know that it is the the length of the ‘opposite’ side divided by the length of the ‘adjacent’ side of a right angle’d triangle.

Pic:

  • Does this have to do with calculating the edge of circles/planes from a point in space, but how? I’ve seen ‘models’ with a tangent component, and they weren’t calculated from a specific light point either.

TL;DR: What does tangents have to do with 3D models? And why/how/where should I use them?