But what is it, the temperature ?

The temperature is a physical value which is mesured with a thermometer.

In daily life, temperature is linked with the hot and cold sensation. what we are sensing are temperatures differences between our body and the exterior environment. If there is a temperature difference, then there is a thermal transfer. The hotter element will become colder, and the colder one hotter.

thermometer graduate Celsius Farenheit
thermometer graduate in Celsius and Farenheit degrees

In physics, we know that particles which compose a material system are never in an immobile state. The more they move, the more there is friction between them, and so the more there is an important dissipation of thermal energy.

Agitation thermique d'une protéine
Thermal vibration of a segment of protein alpha helix(Wikipédia)

In fact temperature is a physical value which define this thermal dissipation and consequently it is an indirect mesure of molecular agitation of a system.