A thermal relief pad is essentially a pad which has fewer copper connections to a plane (such as a ground plane).
A normal pad would simply be connected in all directions, with the solder mask exposing the area to be soldered. However the copper plane then serves as a giant heatsink which can make soldering difficult, because it requires that you keep the iron on the pad longer and risk damaging the component.
By reducing the copper connections, you limit the amount of heat transmission to the plane. It follows of course, that with reduced copper conduction paths, you also have greater electrical resistance. The increase in resistance is marginal compared to the reduction in thermal conductivity.
This should not be a concern unless the pad is carrying high current such that the four traces (on a standard thermal relief) together are insufficient to carry the current; or if it is for high frequency signals where the thermal relief may cause unwanted inductance.