A temperature profile is how temperature of something changes as a function of distance.
In atmospheric sciences, the temperature profile of the atmosphere is how the temperature of the atmosphere changes as a function of altitude above sea level. By looking at the temperature profile of the atmosphere, it is easy to distinguish different layers of the atmosphere.
The figure shows the air temperature as a function of altitude from the ground (altitude 0 km) up to 35 km. This figure is very usefull to understand how air masses are moving in the atmosphere, and why this portion of the atmosphere is separated into 2 parts : the troposphere, from the ground to 14 km where the temperature is decreasing, and the stratosphere from 14 km up, where the temperature is increasing.