Submission is fulfilled by obedience to Allah (عز و جل ) and His Messenger (صلى الله عليه و سلم ) to its rightful requirements, which are the duties that must be performed with sincerity to Allah (عز و جل ) Alone, seeking His pleasure. The evidence for submission from the Quran is in what Allah (عز و جل ), the Exalted, says:

“And turn to your Lord (in repentance) and submit to His (Will) before the torment comes upon you then you will not be helped.” [Az-Zumar 39:54]

And:

“And who can be better in religion than one who submits his face (himself) to Allah and he is a Muhsin (good doer). And follows the Millah (religion/Society) of Ibrahim hanifa. And Allah did take Ibrahim as a khalil (an intimate friend).” [An-Nisa 4:125]

And:

“And whoever submits his face (himself) to Allah and is a Muhsin (performs good deeds), then he has grasped the most trustworthy handhold (i.e. La ilaha illallah)…” [Luqman 31:22]

Also:

“But no, by your Lord, they can have no Faith, until they make you (Muhammad) judge in all disputes between them, and find in themselves no resistance against your decisions, and accept (them) with full submission…” [An-Nisa 4:65]
The Prophet (صلى الله عليه و سلم ) said:
“None of you shall believe until his desires follow what I have come with”. [Reported by Al-Baghavi]