Aqeedah refers to those matters which are believed in, with certainty and conviction, in one’s heart and soul. They are not tainted with any doubt or uncertainty.

The Arabic word ‘aqeedah stems from the root ‘aqada, which conveys meanings of certainty, affirmation, confirmation, etc. In the Qur’aan, Allaah says (interpretation of the meaning):

"Allaah will not punish you for what is unintentional in your oaths, but He will punish you for your deliberate oaths (bimaa ‘aqqadtum al-aymaan)…" 
[al-Maa’idah 5:89]

The verb paraphrased here as "deliberate oaths" is ‘aqqada/ta’qeed, which refers to when one has determination in the heart. It may be said in Arabic, ‘aqada’l-habl (the rope was tied), i.e., it was pulled tight together. The word i’tiqaad (belief) is also derived from this root, and has the meaning of tying up and making strong. The phrase a’taqadtu kadhaa (I believe such and such) means: I am convinced of it in my heart; this is a rational conviction.

In Islam, ‘aqeedah is the matter of knowledge. The Muslim must believe in his heart and have faith and conviction, with no doubts or misgivings, because Allaah has told him about ‘aqeedah in His Book and via His Revelations to His Messenger (صلى الله عليه وسلم). 

The principles of ‘aqeedah are those which Allaah has commanded us to believe in, as mentioned in the aayah (interpretation of the meaning):
"The Messenger believes in what has been sent down to him from his Lord, and (so do) the believers. Each one believes in Allaah, His Angels, His Books and His Messengers. They say, ‘We make no distinction between one and another of His Messengers’ – and they say, ‘We hear, and we obey. (We seek) Your forgiveness, our Lord, and to You is the return (of all).’" [al-Baqarah 2:285]

- and as defined by the Prophet (صلى الله عليه وسلم) in the famous hadeeth which describes how Jibreel came to him and asked him about Islam etc.: "Eemaan (faith) is to believe in Allaah, His angels, His Books, the meeting with Him on the Last Day, His Messengers, and the Day of Resurrection."

So in Islam, ‘aqeedah refers to the matters which are known from the Qur’aan and sound ahaadeeth, and which the Muslim must believe in his heart, in acknowledgement of the truth of Allaah and His Messenger.

IslamQA,  Source: Sharh Lam’ah al-I’tiqaad by Ibn al-Uthaymeen, and al-‘Aqeedah fi-Allaah, by ‘Umar al-Ashqar