What is the maximal path of a tree? Could anyone explain obviously what the maximal path is ? Is it necessary for a tree that has two maximal paths that share no common vertex ?   

It depends what you mean by maximal. Usually maximal is different from maximum in the following sense: a maximal path can mean a path that cannot be made any longer; in other words, at each end there is a vertex all of whose neighbours are already on the path.
Note that under this definition, a maximal path is not necessarily a path of maximum length. Here is one such example ($A-B-C$):
  A
  |
o—B—o—o—o—o—o
  |
  C

