Circulate fan mode is a special fan mode that is used by some HVAC systems which when enabled circulates the air. The fan turns on and then off after a set period of time and the cycle repeats itself so that the air is circulated periodically, but the fan isn’t running 24x7. Some systems also require this for internal operations to keep the coolant moving.
You should use this fan setting only if your thermostat supports/requires that feature. If not you can take a look at this app to replicate the feature.
Ilker, If the beeping started recently it could mean that the battery is low