Bendy Sky Effect? And Free Direction Tunnel?

Hi everybody! The effect I am really curious about is the one that you get in PSone Colin McRae Rally and er, this other, puzzle game I can't really remember where you are a ball rolling along a- never mind. Anyway, the effect is with the sky in the backround which is kind of warped and also wraps around nicely. It looks just like the real sky! I mean it is bent. I'm sorry I can't describe it it technical terms, I'm just a beginner but this is an effect I would like to emulate. Examples in C, Assembler and Basic much appreciated. Or just a description of the algorithm.

Also, if you're not too busy laughing at me for my stupidity could anyone tell me what this means in real *lay* terms, I know it supposed to be easy to understand but I have an A-Level in Maths and I have no clue what it means

"Well, basically the algorithm consists of shooting a ray through each pixel of the screen and check for intersections of this ray with objects in the scene. Let's start with the equation of a ray. A ray is defined as
Origin + t*Direction
where Origin is the vector of the camera, and Direction a normalized direction vector. t is a float that indicates a position on the ray. "

Wha? Could you do a drawing? Vector of the camera as in the direction it faces? As in the position? Is it a number or a matrix? Huh? What? Could anyone give me a SIMPLE SIMPLE explanation?
Thank you in advance.

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