The song is about him being with a new partner and then describing how he can't commit emotionally to that person because he was hurt so badly by his previous (another) love. The song repeats the line "all my tears have been used up on another love" and he describes scenarios that won't be the same as they were with his previous partner.
This is quite a depressing song and therefore i think the video tried to capture that situation whilst adding a twist and happier ending.
The video has him putting up missing posters of a woman which really just represents what's been missing from his life since his old partner. He then finds the woman who represents his new partner, he runs away, not realising that in front of him is everything he is missing from his previous partner... until the end when he finally holds hands with her realising that she is what he's missing.
I like Brianna's answer too though. That could well be the original meaning! Good song.