The word caminar is used mostly for the physical act of walking and not much else.
Yo camino a mi trabajo.
Ella camina a la escuela.
There are some exceptions, of course, but probably not worth mentioning here.
Andar can also mean to walk and in that sense is nearly interchangeable with caminar, although caminar is probably used more commonly.
Yo ando a mi trabajo.
Ella anda a la escuela.
However, as shown here and here, andar also has many other meanings. I'll just list a few:
Yo ando en bicicleta.
¿Porqué anda con una cara triste?
El coche no anda bien, porque tiene una llanta desinflada.
You can find many more examples in the links I provided.
To summarize, caminar is mostly used to mean "to walk". Andar, although it can also mean "to walk", is used more for other meanings such as "to go", "to travel", "to function", "to act", and more.