What a scale actually is
A scale is a row of pitches in order — climbing (or descending) from a home note back to itself an octave later. The home note is the tonic, and every other note in the scale is heard in relation to it: a little way from home, or nearly home, or the note that leans hard back toward home.
That's the important part. A scale isn't a warm-up drill and it isn't the same thing as a key. It's the pitch vocabulary of a key — the notes a piece in that key mostly draws from — laid out as a ladder so you can see the shape.
See it — one octave, tonic to tonic
Eight notes written, seven really — the eighth is the first one again, higher. The ladder goes up by steps (neighbour to neighbour), never skipping. That's what makes it a scale rather than a tune.
Hear it — stop before the top
Play the scale up, but stop on the seventh note and hold it. Your ear will try to finish it for you — it wants that last step home. That pull is the whole reason keys exist.
Try it
Try
Play a one-octave G major scale slowly, up only. Stop dead on the F♯ (high 2 on the D string) and count four slow beats before you play the last G. Feel the itch to move. Then do it again stopping on the E (the sixth) — less itch. Then on the D (the fifth) — you could almost rest there. The scale's notes are not all equal.
A scale is not a key
Same eight notes, two different homes. Play this — it circles C and sounds settled on C:
Now the same seven notes, arranged around A instead — and it sounds like a different piece, in a minor key:
The usual mistake
Treating "scale" as a synonym for "boring exercise". A scale is a map — practise the G major scale and every piece in G major is half-learned, because you've already found every note under your hand and heard how each one pulls. The other mistake is thinking the scale is the key. The scale is the ladder of notes; the key is the sense that one of them is home. You need both words.