I've seen Doctor Strange but I didn't understand why the cape chooses Stephen.
I know that the cape is his Relic. Please answer in detail.
You're going to be let down, because there is no "in detail" answer to this. The cloak, of it's own will, simply deems Dr. Strange "worthy". For an unknown reason, which is never explained, the cloak chooses him. And that's it.
There is not much detail to point it out here, according to the Cloak of Levitation Wiki, the cloak simply chooses Dr.Strange.
Many relics choose their owners, and this was the case with Dr. Stephen Strange when he was deeply entrenched in battle with the rogue sorcerer Kaecilius in the New York Sanctum.
It's not like Thor's hammer
Thor's hammer can be picked by anyone who is worthy at anytime (Vision already showed us that in Age of Ultron). The cloak already chose Strange so it can't be worn by anyone else.