Things that last forever never come to an end — they continue endlessly. An experience that changes you forever alters you in ways that will last the rest of your life.
The adverb forever literally means "eternally," so when you promise, "I'll love you forever." you mean it. You can also use forever in a less literal, more exaggerated way: "It is taking forever for the bus to get here," or to mean "without stopping," as when you comment that the rain can't continue forever. The word combines for and ever, which stems from the Old English æfre, "always."