When a given situation has no solution.
It makes reference in the form of a parabola to someone who has lost his mental health and has no cure.
It is said that people without cure to a mental disease used to be sent to a mental health care facility for life where they would manufacture baskets for the rest of their lives.

1) Someone who is going mad or on the verge of a nevous brakedown.
2) A Green Day song sung by the one and only Billie Joe Armstrong. Arguably one of the great Green Day songs, if not one of the great songs of the 90's.

The phrase has its roots in WW2. When a soldier came into a medical facility with a limb or multiple limbs detatched from his body, the nurses would call the patient a "basket case". As in they had to bring the soldier to them in a basket.

Modern day usage is to describe someone that is in need of extreme assistance(mental or physical).

some one that has a bunch of problems and mental and phycoloically

The term has its roots in world war I. The soldiers referred to the injured who had to have all four limbs amputated as a basket case. I figure it is something to do with the fact that the person will now have to be carried around in a basket!

someone whos emotions are filled with anxiety and obsession

a very nervous and distraught person(Formerly used to refer to someone who is totally physically disabled. See also nervous wreck.)