Bottom-Up Parser With Leftmost Derivation
"Linearizing" here is equivalent to superimposing a total ordering on what is a partial order. If your grammar is context-free, this partial order can always be conveniently represented by a tree. Other types of grammars will be able to produce derivations orders that are not tree-like, and that is why we generally avoid them.

This total order is meant to allow for sequential algorithms to be written, because the input will be read sequentially. That's all, no magic here. 

What happens is that different criteria for linearization will serve different algorithms: if you are going to reduce the input, you will go "from the bottom up", metaphorically, so the linear order that suits you (if you are reading the input left-to-right - because your language has an indo-european flavor), is postfix. If not, prefix.