strain
When you stretch a rubber band it gets longer. Strain measures HOW MUCH it stretched compared to how long it was to begin with. Stretching a 10 cm band by 1 cm and stretching a 100 cm band by 10 cm are, in a real sense, the same amount of stretch — each grew by one tenth of itself. Strain captures that fair comparison by dividing the change in length by the original length.
Engineering strain is epsilon = (L - L0) / L0 = delta-L / L0, where L0 is the starting length and L the stretched length. It is a pure ratio with no units (a length divided by a length), so it is often given as a percent or as a small decimal. Example: a bar 50 mm long stretched to 50.05 mm has strain = 0.05 / 50 = 0.001, or 0.1 percent. Elastic strains in stiff metals are tiny — often well under 1 percent — while a rubber band can strain by several hundred percent.
Strain is the natural partner to stress: plot stress against strain and you get the stress-strain curve, the single most useful fingerprint of a material's mechanical behaviour. A caveat mirrors the one for stress: engineering strain divides by the ORIGINAL length, which is fine for small elastic stretches but understates the real deformation once the material stretches a lot, so large-deformation work uses true strain instead.
A guitar string 640 mm long is tuned up and stretches by 6.4 mm. Its strain is 6.4 / 640 = 0.01, one percent — a big strain for steel, which is why the string is under so much tension.
Strain is a fraction of the original length, so it has no units — quote it as a decimal or a percent.
Strain is dimensionless — a stretch relative to the starting length, not an absolute distance. Reporting 'it stretched 2 mm' is meaningless without saying 2 mm out of what starting length.