Thermometer resolution refers to the smallest increment of measurement readable from it. A thermometer that displays temperature readings to the hundredth of a degree, e.g. 30.26° has a greater resolution than one that only shows the tenths of a degree - e.g. 30.2°, or whole degrees 100°.
Although resolution differs from accuracy, the two should be thought of as going hand in hand. A thermometer that is accurate to ±0.05° wouldn't be half has useful if its resolution were only in tenths of a degree, e.g. 0.1°. Likewise, it could be misleading for a thermometer to show hundredths of a degree on its display, if it's traceable accuracy were only ±1°.
Sometimes the resolution of a given thermometer changes above or below a certain temperature. The ETI PTR Printing Temperature Recorder, for example, has a resolution of 0.1°C up to 299.9°C and a resolution of 1°C after that temperature point, all the way up to its maximum range of 1372°C. A thermometer that automatically adjusts its resolution at the critical temperature, like this, is said to be auto-ranging.
In rare cases, the resolution of a thermometer can be affected by the limitations of its digital display—older thermometer models often only had space to display three digits, so even though the thermometer and probe were precise to the tenth of a degree, after 99.9° or -99.9°, only whole digits were displayed - i.e. 100° or -100°.