The physics behind it all
Law of Reflection
It is usually very easy to predict how light will behave. The simpliest interaction of light between a plane mirror is it simply reflects off, and it will always travel in straight lines. The most principle "law" is the law of reflection, which states that light will reflect off a plane mirror at the same angle at which it hits it. In other words, the angle of incidence is equal to the angle of reflection.
Concave Mirrors: Rules of Reflection
Light reflecting off a mirror is a little more complex. To draw ray diagrams of how light reflects, simple follow the two rules:
1. Light traveling towards the mirror parallel to the optical axis will reflect and pass through the focal point of the mirror (green ray)
2. Light traveling through the focal point towards the mirror will reflect off, traveling parallel to the optical axis (yellow ray)
Concave Mirrors: Focal Point
The focal point of a concave mirror is the point where the most light will converge, due to the two rules of reflection stated above. For speherical mirrors, the focal point is usually a length of half the radius, measuring from the deepest part of the mirror. This is the point where you will get the most light and is the optimal point for lighting stuff on fire.
Fire
The Law of Conservation of Energy is one of the conservation laws which states that energy cannot be created nor destroyed, but instead changes form and type. In our case, we are witnessing light energy being converted to heat energy on the surface of the object being held in the focal point. The main concept behind this is light and colour. Colour is perceived as a specific spectrum of light being absorbed into an object.
For example, consider a white ball and a red ball. When light is shining on the white ball, all the light is bouncing off the surface off the ball and therefore you see no colour. When light is shining on the red ball, light still bounces and reflects off the surface, but all the red parts of the light is being absorbed into the surface. Everything else (blue, yellow, green, etc) is being reflected off the surface, and that is how you are able to physically see the ball. The red part of the light remains "absorbed" into the ball, and so that is the colour that you see.
Now, what happens to the light that is absorbed into the ball? According to the Law of Conservation of Energy, light energy cannot simply stay in there or disappear -- the ball has to get rid of the excess energy somehow. What happens is the light energy is converted into heat energy, which is then dissapated into the atmosphere. As more and more light is being shone onto the ball, more and more red parts of light is being absorbed, more and more light energy is converted into heat energy, and the ball gets hotter and hotter. Eventually, with enough light and heat, the ball will reach it's flash point and catch on fire.