Felt air temperature is a quantitative measure that indicates the amount of heat the human body loses outdoors in a given time and place.

It is an indication of the air temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 perceived by the body, which may differ from the actual temperature due to other climatic conditions affecting the exchange of heat

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

 between the body and the air.

The factors contributing to the felt air temperature are air humidity, density, and the speed of wind at five feet (1.5m) from the ground where the average human face is.
The ability of the air to absorb heat is affected by its relative humidity

Relative humidity

Relative humidity is a term used to describe the amount of water vapor in a mixture of air and water vapor. It is defined as the partial pressure of water vapor in the air-water mixture, given as a percentage of the saturated vapor pressure under those conditions...

, and its density.
The faster air blows over a surface, the more air is brought into contact with that surface in a given time interval, increasing the heat loss or gain of the body.
This is reflected in the wind chill

Wind chill

Wind chill is the felt air temperature on exposed skin due to wind. The wind chill temperature is always lower than the air temperature, and the windchill is undefined at the higher temps...

 referring to the reduction of felt air temperature resulting from the wind.

Feels like is a meteorological

Meteorology

Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

 expression used in weather forecasting

Weather forecasting

Weather forecasting is the application of science and technology to predict the state of the atmosphere for a given location. Human beings have attempted to predict the weather informally for millennia, and formally since the nineteenth century...

and weather reports referring to the felt air temperature.