Birthdays are a special time in Judaism, to the point that it is considered that the Mazal - the soul - is stronger.
We see in the Torah itself the idea that one should celebrate one's birthday, from the story of Pharaoh, the king of Egypt, and Joseph, the son of Jacob. The Torah relates that on his birthday, Pharaoh threw a party!
There are different customs, among which are giving a little more Tzedakah than is given daily, studying the chapter of psalms corresponding to the person's age, and taking stock of the past year, making good resolutions for the coming year on the three pillars on which the world is based: Torah (its study), good deeds (which include Tzedakah and the observance of Mitzvot in general), and prayer (which includes service to God in general).