To celebrate means to mark a special day, event, or holiday. You might celebrate a birthday, a religious holiday, or even the anniversary of a famous battle.
Use celebrate for festive, happy occasions. If the special day, event, or holiday is more solemn or introspective, a verb like observe is often used. After we observe Memorial Day, we look forward to celebrating the Fourth of July. The verb can also mean to honor or praise — "The book celebrated the life of the actress who had given so much to worthy causes."