Really there is no difference between "get something done" and "have something done".

As Tony said, it normally refers to something that someone else will do for you.

You could change each of the words <em>get</em> or <em>have </em>in Tony's examples:

I will get my car washed (someone will wash my car)

I will have my hair cut (a hairdresser will cut my hair)

I will get a dress made for the wedding (a dressmaker will make a dress for me)

I will get the house painted (a painter will paint my house)

I will have my eyes checked (an optician will check my eyes)

I will have my dog neutered (a vet will castrate my dog)

to have/get something done

Please, is there someone who can explain this expression to me?

To have or to get something done usually means to ask someone or pay someone to do a task for you.

For example:

I will have my car washed.

I will get my hair cut.

I will have a dress made for the wedding.

I will have the house painted.

I will get my eyes checked.

I will get my dog neutered.

etc.