You didn't make it. But you were close to making it. For example: "I needed a score of 60% or more to pass the test, but I only got 59%. I almost made it."

It a nicer way of saying "I failed"

Think of almost as 差点儿： I almost made it = 我差点儿通过 I almost won = 我差点儿赢了 I almost forgot = 我差点儿忘了