In more detail
A common way to compute it is the Magnus approximation, with T in °C: γ = ln(RH / 100) + 17.62 × T / (243.12 + T), then dew point = 243.12 × γ / (17.62 − γ). Unlike relative humidity, which changes as the air warms or cools, the dew point tracks the actual amount of water vapour in the air. It can never be higher than the air temperature; when the two meet, relative humidity is 100% and dew or fog forms. When the dew point is below freezing, moisture deposits as frost instead.
Why it matters
Dew point is the better guide to comfort: below about 13 °C (55 °F) air feels dry or comfortable, above about 21 °C (70 °F) it feels oppressive. Forecasters use it to predict fog and how low the night temperature can fall. Condensation forms on any surface colder than the dew point, which is why cold pipes sweat and why painters avoid coating a surface that is close to it.
Example
Air 25 °C, 60 % RH → dew point 16.7 °C
Same air warmed to 30 °C → RH 44.8 %, dew point still 16.7 °C
Same air cooled to 18 °C → RH 92.1 %
Air 30 °C, 40 % RH → dew point 14.9 °C (drier, despite the heat)