DIAGNOSIS That's the internal relay clicking. It's the physical switch inside the thermostat that turns your HVAC equipment on and off. You're hearing it engage or disengage. While some click on a major mode change is normal, frequent clicking every few minutes is usually the system short-cycling.
FIX Short-cycling is bad for your compressor or furnace. The main setting to fix this is the 'Minimum Cycle Time'. On your thermostat, go to Menu > Settings > Installation Settings > Thresholds. Look for 'Compressor Minimum Cycle Time' (for AC/Heat Pump) or 'Minimum Heat Cycle Time' (for furnace). Increase this value. For AC, try setting it to 5 minutes. For a gas furnace, 5-10 minutes. This forces the system to stay off for that long after it shuts down, preventing rapid on/off cycles.
IF THAT DIDN'T WORK The clicking might be from the 'Differential Temperature' setting being too tight. This is how much the temperature can drift from your setpoint before the system kicks on. In the same Thresholds menu, find 'Cool Differential Temperature' and 'Heat Differential Temperature'. The default is usually 0.5°F. Try widening this to 1.0°F. This gives the system more 'breathing room' and reduces the frequency of starts.
HEADS UP If the clicking is a loud, single *clunk* when the heat first comes on, that's probably not the thermostat—that's likely the ductwork expanding from the warm air or a damper in your system. The thermostat relay click is a softer, sharper, electrical sound.