Each thermostat model has a different display message when a delay occurs. This delay can be up to five minutes under normal operating conditions. A delay is used to protect your heating and cooling equipment from coming on too quickly (known as short cycling), which can cause damage.
The thermostat has a built-in compressor protection (minimum off timer) that prevents the compressor from restarting too early after a shutdown. The minimum off timer is activated after the compressor turns off. The thermostat keeps the compressor off for a few minutes before restarting, to prevent equipment damage.
If the delay lasts longer than five minutes, there may be an issue with the voltage to the thermostat. A professional contractor could verify that the voltage is within an acceptable range and that there are not shorted wires.