It's similar to "said", but it implies that the person is stating a fact (or something that they believe to be a fact).
It has more "finality", or weight, than "said".
"Stated" is somebody making a "statement".
"We are lost," said Andrew.
"We are lost," stated Andrew.
The 1st one is just Andrew saying "we are lost".
The 2nd one gives the reader the sense that Andrew is 100% sure they are lost, and he is stating that fact.
Hope that helps a little bit.