Mark Rothko: “A painting is not a picture of an experience, but is the experience.”
Rothko is one of the most influential figures in the world of abstract expressionism. He is known for his use of vivid colors and dramatic, expressionist paintings. It is said that he used color to help convey his emotional state, as well as to portray an emotional reaction on the parts of viewers. He used color to evoke strong emotions in people so they would feel something.
Because of the way Rothko orchestrated his paintings, he is known to have used color to help people identify with his work. Modern art is all about reacting emotionally to what you see, not necessarily logically figuring it out. Looking at Rothko's paintings is like looking into his heart, it brings emotion to the surface - but different people will undoubtedly feel different things upon viewing.
“If you’re looking at a painting by Rothko, you need to give it time, so that you can almost lose yourself within that canvas… You can’t walk by a Rothko and get very much out of it. But if you spend the time to immerse yourself within it, that’s when there’s a reward.” -Gwen Chanzit, Curator
Source: Singular Art
While there isn't always a correlation between the meanings of paint colors and what they are intended to evoke, he definitely used color to help people relate to his work on more than just a rational level. Rothko had many different color schemes throughout his life, but especially reds and blues. He also used white paint a lot because it represents purity and spirituality to him. He made it clear that there was meaning behind his art, but assigning meaning is up to the viewer.
This is an interesting theory on why people are moved by art - it's not always about seeing something that makes you feel something deep down, or about feeling like you can relate to something in it. Some people just like looking at art because they enjoy looking at beautiful things. The experience is different for everyone and that in itself is a beautiful thing.
Look around, and absorb all of the art you can. The more you have an understanding of color theory, the stronger your inner-senses will become.