These two are frequently used incorrectly and it can be distracting to the reader. Past can be a noun that refers to a period of time that has already happened (He wants to live in the past), or it can be an adjective describing something that has already happened (He wants to relive his past glory. Most frequently, it is an adverb describing a verb: He walked past the dining table.
Passed is the past tense of the verb pass and can be used in a number of ways. To move beyond: We passed the entrance and had to double back. To achieve: I passed my test. To die: He passed away. To cease: The feeling soon passed. In sports, to transfer: He passed the ball.
There are several other ways the verb pass may be used, and all meanings are easily accessible in any online dictionary. But the most frequent difference between these two words is the distinction between the verb and the adverb. Remember, you walk past something, but you pass it. The same thought can be expressed either way: He walked past the store. He passed the store.