Why it matters
A hydrometer floats according to the density of the liquid, and liquid density changes with temperature. Warm wort is less dense, so the hydrometer sinks further and reads low. The instrument is calibrated at one temperature — usually 20 °C, sometimes 15.6 °C on older or American models — and every other temperature needs a correction.
Check the stem or the paperwork before trusting the default. A 4 °C error in the assumed calibration point is worth about a point of gravity.
The correction
How big is the error?
Small at ordinary temperatures and large at brew-day ones. A reading taken at 30 °C when the instrument expects 20 °C is roughly 2.6 points low. At 60 °C — straight out of the mash tun — the error is well over ten points, enough to make you think a mash failed when it did not.
A practical note
The correction is reliable within maybe 20 °C of calibration. Past that it is an extrapolation, and a hot sample brings other problems: the wort is still changing, the reading drifts as it cools in the cylinder, and hot liquid in a glass tube is a poor idea generally. Cool the sample when you can, and use the correction for the last few degrees rather than the first fifty.