I can't give you a particularly scientific or mathematical explanation but it's basically the engine putting all its factors into the melting pot (material, pawn structure, king safety and all the others you can think of) and spewing out it's result. Whereas a human might say White is slightly better, the engine might say +0.35 or whatever. Different engines give different weightings to different factors which is why you might get a discrepancy in evaluation between two or more engines.
Of course if there's a forced tactical sequence (or a mate) then engines will all display much the same output and eval.
when i look at the analysis from chess engines they display a number, i know if X<0 is for blacks advantage, and if X>0 is whites.
where do these numbers come from? how are they calculated. i've searched google but haven't found anything that explains it, maybe i'm using the wrong search terms. either way i'm highly curious about this.