"Perspective" is literally the term for a technique used by artists. In real life, railroad tracks are parallel and are always 1.435 meters apart. An artist draws them as coming together and meeting at a "vanishing point" on the horizon. In real life, people are all about the same height, but in a picture, a person who is farther away is drawn smaller than a person who is close up.
So, "perspective" can literally mean "drawing things smaller if they are further away."
"Putting something into perspective" can mean "drawing something the appropriate size, according to the rules of perspective."
Figuratively, "put it into perspective" means "it's not that important, don't make it out to be such a big thing, treat it as a small thing... like a distant object in a picture."
An opposite figure of speech is to "lose your sense of proportion" or "blow something out of proportion," meaning to take something small and unimportant and treat it as much more important than it is.
"Hey! They didn't ring up my grocery bill correctly! These were supposed to be on sale, two for $1.95, and I was charged $0.99 each. I have to go back to the store and get this correct."
"Relax. Put this into perspective. It's only a difference of three cents."
"But it's the principle of the thing! I was cheated! Robbed!"
"I think you're blowing this completely out of proportion. It's not worth it. Let it go."