Centripetal force

The centripetal force is directed on an object in a circular motion towards the center of the circle. We were given a helpful packet with equations and explanations. On the quiz, I did pretty well. I got all the momentum questions right and on the centripetal part, for acceleration I did 4pi^2/t which it should've been t^2. I guess what sort of confuses me is where the force comes from. Like if you think of a runner on the track, the friction is the centripetal force. Its a little confusing that the friction causes the runner to go inwards, but if you think about it, the runners natural tendency would be to go straight. If you look at the diagram above, the runner would follow the path of inertia, but due to friction it doesnt. But this is still confusing I'll be honest. In the picture above is the force coming from the string or the person?
Im decent with calculations and what not because the equations are given. So if the question is asking for velocity, you plug the known information in one of the given equations, but its understanding the equations, and breaking them apart to figure out where they're derived from is what is difficult for me. I feel like I have a general understanding of centripetal force, but I need to work towards a deeper one.

The flying pig, here is a picture of our work. We were trying to find the force on the string and this involved many different equations such as the pythagoreum theorum and the force equations. We had to find the force on the string, so as you see we drew a force diagram. We decided to find the earth force (mass) and the centripetal force, and then with our vector knowledge, we could use the pythagoreum theorum to find the hypotneuse aka the force on the string.