A scale is simply a series of notes played from a starting point, progressing in ascending order, and ending one octave from the starting point. It can also continue into the next octave or descend back to the starting point. Most scales move from one note to the next by either a whole step or a half step. The thing that distinguishes one scale from another is the exact sequence of whole and half steps.
Probably the simplest scale to learn and understand is the chromatic scale. A chromatic scale can start on any note and ascends one half step at a time. You play all 12 notes before you end an octave above the starting point. An easy way to play this on the guitar is to start with the low E string (6th string) and play it open, 1st fret, 2nd fret, 3rd fret, etc. continuing to the 12th fret. You have just played the notes E, F, F#, G, G#, A, A#, B, C, C#, D, D#, and E. A more efficient way to play this on the guitar would be to play only up to the 4th fret on the E string, change to the A string (5th string) and play up to the 4th fret, then change to the D string (4th string) and play up to the 2nd fret. The best way to finger this with your left hand is to play in 1st position. This means using your 1st finger at the 1st fret, 2nd finger at the 2nd fret, 3rd finger at the 3rd fret, and 4th finger at the 4th fret. This way your left hand is not sliding up or down the neck (changing positions).
The chromatic scale is not particularly useful in terms of composition or harmony but can be a great coordination exercise if you combine the right hand technique of alternating picking, either with a flat pick alternating down strokes with up strokes, or using two fingers alternating the index finger with the middle finger. See the diagram in the article The Chromatic Scale in the Exercises section.
A close relative to the chromatic scale is the whole-tone scale. This scale would be a sequence of whole steps, which would only have six different notes in it (E, F#, G#, A#, C, D for example) and is even less useful than the chromatic scale. See the additional articles about other specific scales and modes.