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A gravitational wave's strain (GW strain, h, or in context, just strain) is a measure of its effect, specifically the ratio by which lengths are stretched or compressed, which is a dimensionless number. The term strain might be used to refer to various particular measures: to the observed strain (as measured by a gravitational-wave detector), or to the strain in the direction of the wave's displacement. Also, the term can be used for the peak strain of the wave (its amplitude), or for the instantaneous displacement (at a point in time). The following two relations are often cited:
h ≈ ΔL/L h ≈ ΔT/T
These are sometimes cited with "=" or "∼" instead of "≈", the latter of which is sufficiently loose to be strictly true whether referring to the observed strain or the wave's actual amplitude. The relation based on T represents a shortcut when relative distances are measured by measuring time intervals, such as when using pulsar timing (pulsar timing arrays).
A variant term, characteristic strain (hc), which is sometimes what is intended by strain, is often used in general discussions: it is a kind of averaging (i.e., something like RMS, in that it doesn't merely average to "zero" over each wave period), which includes a component varying by frequency. The term is often used when explaining relative detector ability and source strength over the gravitational wave spectrum.
The strains measured by the GW detectors (e.g., LIGO) peak at on the order of 10-21 (i.e., a meter-distance of space is lengthened and shortened by about 10-21 meters). By my calculation, this strain applied to the distance from here to the Sun is about 1/6 nanometer, and to the distance from here to Alpha Centauri is about 1/25 millimeter. LIGO measures (near-infrared) light-travel over 4-km arms, and by repeatedly reflecting the light over this distance, it measures the strain on a distance of about 1200 km. Given a 10-21 strain, the distance-change LIGO measures is roughly a tenth the width of a proton. LIGO's sensitivity is actually about two orders-of-magnitude better than that: it measures the changing instantaneous strain over the course of each gravitational wave period.