We're in the middle of the twentieth century, when abstract art was exploring how basic forms and bold colours can represent the world around us, or make us feel. Mark Rothko was an important part of a movement that built on the structured geometries of Mondrian decades before, but went further from the representational, deep into the abstract. His big bold panels of colour evoke quick emotions and visceral responses.
This piece above is from 1950 and is called "Number5/Number22" A big stripe of vibrant red through the yellow and gold, and the scratched away red. Is it a foreground, a horizon and a setting sun? Is it the close-up of a commercial logo or label? It's left to us, but we certainly feel something in its bold colour and strong shapes.
About these pieces Rothko said he wanted us, the viewers, to feel "the tragedy, ecstasy and doom." It's about the extremes of emotion and thus the strong, deep colours and shapes.
Rothko too explored a variety of styles in his earlier works. He did slightly more representational stuff in the '30s and '40s but settled soon on the blocky shapes and colour blocks for which he's remembered.
I see a strong influence of Kandinsky in some of Rothko's mid-1940s pieces. There are a number of surrealist-looking 'untitled' pieces. One called "Slow Swirl at the Edge of the Sea (1944) explored a similar style to the one I've pasted here, which is called "Archaic Idol" (1945) Compare this and those other contemporary pieces to Kandinsky's 1920s abstracts. Here is Kandinsky's "Small Dream in Red" from 1925. Was this a major influence on Rothko's early exploration of shape and colour? Probably. 
Scrolling through Rothko's chronological works through the late 1940s and into the 1950s is very illustrative of his evolving approach. In this image here I've reduce down to postage-stamp sizes a view of his work from the mid 1940s to the mid 1950s.
Isn't that interesting? By the end the shapes become bigger and the detail is reduced, one might say, to pure emotion.
In conclusion I give you these two pieces. The red with white and black is "No. 46 (Black, Ochre, Red Over Red)" (1957) and the orange and yellow piece is called, strangely enough, "Orange and Yellow" and was completed in 1956.
If these pictures, and their price tags make you angry, might I suggest you explore the works of Barnett Newman? He'll really piss you off.
