Sincerity in all we do is a commandment of Allah:
"Say, 'Indeed my prayer, my rites of sacrafice, my living and my dying are for Allah, Lord of the worlds. No partner has He. And this I have been commanded and I am the first among you of the Muslims.'" -Surah al-An'aam ayat 162-163
"And they were not commanded except to worship Allah, sincere to Him in religion, inclining towards truth and to establish the prayer and to give zakah. That is the correct Deen." -Surah Bayyinah ayah 5
Abd al-Qahir al-Jurjaani rahimullah defined ikhlas as "not seeking any audience for your deeds other than Allah."
We're warned throughout the Qur'an and Sunnah to have sincerity in tawheed of Allah, sincerity in our intentions, sincerity in our tawakkul (placing of trust and reliance) in Allah, sincerity in our worship (i.e. salah, sujood, du'a, siyaam/fasting, Hajj, zakah, sadaqah, tawba, Jihad, recitation of al-Qur'an, etc.) and sincerity in all our actions and words.
Al-Fudayl ibn 'Iyaad rahimullah addressed his students on one occasion about Surah al-Mulk ayah 2 that's interpreted to mean: "He who created death and life to test you as to which of you is best in deed." Noting that "It is those deeds which are most correct and most sincere. If a deed is done sincerely, yet is not done correctly, it will not be accepted. And if a deed is done correctly, but not sincerely for Allah, it will not be accepted. It must be done sincerely (for Allah alone) and correctly (in accordance to the Sunnah).
BEWARE THE ANTAGONISTS OF IKHLAS! They are three:
Riyaa is to perform an act of worship to show off to people; seeking their praise or some other vanity.
Sum'ah is to speak good for the sake of people's compliments or praise.
'Ujb is a sitatuation where one becomes impressed with his/her self for the good deeds they've done.
Ibn al-Mubarak rahimullah said: "Perhaps a great deed is belittled by an intention. And perhaps a small deed, by a sincere intention, is made great."
May Allah, Mighty and Exalted is He above having any partner, equal or opponent, make us all among His mukhliseen (sincere slaves) and keep us aware and resistant of those diseases that corrupt our righteous actions and convert them to arguments against us on the Day of Accounting. Ameen.
Ya'qub al-Makfuf (may Allah have Mercy on him) would say: "The sincere one is he who hides his good deeds in the same way that he would hide his bad."