What response time is?

With response time in general the time required for a system to react to an external modification is defined, in particular to reach a certain level of such modification.

Speaking of a sensor system, for example a temperature data logger, the response time of the temperature sensor is the time taken to warn the modification of the temperature to which it has been set. The heat exchange between the sensor and what is measured takes time because it is completed and this is why there is always a delay, more or less important, in detecting the real temperature in that actually shown by the sensor.
The response time in particular is that time required by the sensor, after a thermal "jump" (speaking of a temperature sensor, for example), to detect a part of this "jump", that is of this variation. This part is expressed with a percentage of the jump and is generally 90%: this is why it is called T90. Sometimes, other percentages are taken into consideration, such as 50%, and we talk about T50.
Taking a theoretical example, under ideal conditions, if we take a temperature sensor that is at 0 ° C and we immediately put it in an environment at 100 ° C, the T90 is the time that the sensor takes to detect 90 ° C, that is 90% of its temperature difference from 0 ° C to 100 ° C.

The same can obviously be done for any other type of sensor: humidity, pressure, etc.