the adjoint representation of a Lie group

Hello! Can someone please explain to me the concept behind the adjoint representation of a Lie group? I have run through the theory but I ma not quite getting it.

In my book the author gives such definition

''Take any $\displaystyle a\in G$ and define homomorphism $\displaystyle ad_{a}:G\rightarrow G$ by conjugation

$\displaystyle ad_{a}:g\mapsto aga^{-1}$

This homomorphism is called the adjoint representation of G''

What does it do?

I have also noticed that there is also an adjoint representation of a Lie algebra? what is the difference?

Thank you