To "put things in perspective" means to see them from an objective viewpoint.
For example: A young person may be emotionally devastated by a breakup with a boyfriend or girlfriend. The best way for that person to get over the hurt, is to see the relationship from the viewpoint of his or her whole life, rather than just for the present. While no one should deny that a breakup always causes hurt feelings, anyone who has lived through a breakup can tell you that it is not the end of your life, and the best thing to do is continue living and dreaming of your future. That would be "putting things in perspective".