How to Explain Time Constant in Simple Terms and Its Role in Electrical Transients

Hello. What is this time constant, by the peasants' mind? (in relation to transients) I cannot understand this concept for a Christmas tree and google does not offer me anything specific. Please help with clarification. I will answer this tomorrow, and I don't know how to explain the time constant and its practical application.

Quarz wrote:

The time constant is the time after which a steady state occurs in the circuit, if the speed of changes taking place in a given circuit and going to the steady state was the same as at the beginning of this process

https://www.elektroda.pl/rtvforum/topic627925.html#4524880
https://www.elektroda.pl/rtvforum/topic583030.html#3013685

Hello!
See the drawing:

If from a source (e.g. a battery) with a voltage U, a current flows through the resistor R to the DISCHARGE capacitor C, then the voltage on its electrodes will start to rise according to the diagram in the figure.
The rate of voltage rise depends both on the resistance of the resistor R and the capacitance of the capacitor C. The product R * C is called the time constant, and the special property of this time constant is such that after the time T = RC on the capacitor there will be 63% of the steady voltage U, to which the capacitor will be charged after the INFINITELY time, but in practice we assume that it will be after a time equal to a few time constant (after a time equal to 10 time constant, the difference is only 0.0005%).