I think it was made pretty clear when Itachi explains it to Naruto when he was Edo Tensei.
Itachi and Shisui both new a Civil War was on the cards since Uchiha were plotting a Coup. Both having grown up in the era of great war didn't want it to come to that. Shisui tried to use his Genjutsu prowess on the village elders to stop the anhilation of Uchihas, but Danzo overpowered him and stole his eye. Shisui managed to get away but lost an eye. He didn't want any other power monger to get hold of his other Mangekyo Sharingan and thus entrusted it to Itachi, because he knew he believed in the same ideals. He left the village and faked his death.
On a smartphone. So will edit with proper citations of manga chapters later. Please take a look at Wikia. It should explain it more clearly
Edit 1: For those convinced he commited suicide
Shisui wrote a suicide note telling his clan he cannot follow through with the coup d'etat, but his clan's narrow mindedness made them unable to understand this, believing he would even sacrifice innocent lives for the sake of the Uchiha Clan. The contents of the suicide note also made it appear as though he had crushed his eyes when jumping off a cliff into the Naka River to kill himself in order to prevent conflict from arising over his eyes within the clan. He, at the same time, was able to erase his existence, leaving no corpse behind.
Wiki Source: Chapter 550 pg11. Chapter 520 pg 15
Edit 2: I am not sure whats wrong with people, but they do not want to do their own research but will hold their beliefs and opinions as hard facts. I am open to different interpretations of said facts BUT don't refute the facts. Here is the anime clip of Shisui giving his eye to Itachi (Not that itachi killed him and took his eye)