Jerusalem is Israel's capital in every historical and practical sense.
King David made Jerusalem the capital of his Kingdom some three thousand years ago; and since then, Jerusalem has been the capital of every Jewish entity, until its destruction by the Romans in 70 CE.
Jewish independence was restored in 1948 with the establishment of the State of Israel, and Jerusalem was declared once more the capital of Israel. This decision, enshrined in a Basic Law (1980), has practical implications. Jerusalem is the seat of all the symbols of Israeli sovereignty: the President of the State, the Knesset, the Government, and the Supreme Court.
Most countries do not recognize Jerusalem as Israel's capital; the reasons for this are political, and they ignore the basic right of every state to determine its capital. The State of Israel has exercised that right and determined, very naturally, that its capital is Jerusalem.