Good, basic question.
Flashing is the process of installing the ROM; it's just the word that's used because you're affecting the deeper portions of the system, actually replacing most of it.
Getting familiar with the menus in the recovery area is a great way to begin to understand rooting.
Wiping paves the way for a fresh ROM install. Sometimes it is not necessary and you will see developer notes saying that.. most often when upgrading from one version of a ROM to another of the same ROM.