CAT tool: Computer Aided (or Assisted) Translation tool. Strictly, any computer-based tool used as part of the translation process, but commonly used to refer to translation memory (TM) programs.
Editing (revising): checking a translated document against the original for accuracy, style, etc.
Proofreading: checking a document in one language for spelling, grammar, punctuation, etc.
Source language: the language your document is written in.
Target language: the language you want your document translated into.
TM: Translation memory (program): in very simple terms, a TM program splits your text into segments (sentences or parts of sentences) and stores the translation for each segment; if the same segment comes up again later in the same text or even in another document, the program suggests the previous translation so that it can be re-used. Useful for repetitive texts and sets of documents with similar content, to help with consistency.
Translation: transferring the meaning of written documents from one language to another.