A scale is defined by Naxos, the widely respected online classical music database, as “a sequence of notes placed in ascending or descending order by step.” The key words in this definition are “sequence,” meaning the order of the notes is essential in identifying the scale; “ascending or descending,” meaning the scale has a single definite direction in pitch-space; and “step,” meaning the scale moves by one letter name at a time (i.e., C to D to E to F, etc., instead of C to E to G, etc.).
As an aside, that definition of a scale is flexible and is, for 21st century intents and purposes, obsolete. We’ll get to that later in the section on Synthetic Modes and Other Advanced Scale Topics. For now, accept Naxos’s description as a working definition.
So: a string of notes, in a certain order, going in one direction, advancing by step. Different scales are identified by the number of notes and the size of the steps between consecutive notes.