Strain measures deformation relative to the original size of a body, so it is dimensionless.

Normal strain

For a bar with original length $L$ that changes length by $\Delta L$, the average normal strain is

$$\varepsilon=\frac{\Delta L}{L}.$$

Positive normal strain represents extension; negative normal strain represents contraction.

Shear strain

Shear deformation changes angles. For small deformation, engineering shear strain $\gamma$ measures the change in angle between lines that were initially perpendicular.

A simple block displaced sideways by $\Delta x$ over height $h$ has approximately

$$\gamma\approx\frac{\Delta x}{h}.$$

Strain and displacement

Displacement tells how far points move; strain tells how those motions change distances and angles within the material. A rigid translation can therefore have displacement without strain.

Stress describes internal loading, while strain describes the resulting geometric deformation.