What is meant by "Group delay"?in simple words?
Here is my simplest explanation:
The group delay, as the negative derivative of phase, predicts the time delay of the amplitude envelope of a pulse, as shown in the hand-drawn graphic below. The upper part of the sketch shows a sinusoidal waveform varied in amplitude by its envelope. The lower one is showing this same envelope before and after a system that has group delay.
This applies when the phase of the frequency response can be approximated as linear for the &quot;group&quot; of frequencies within the pulse envelope. Thus for non-linear phase systems, this applies to generally narrower band signals such as the pulse I show where the amplitude transition is gradual.
Consider a single sine-wave with the amplitude envelope such as I show. The time delay of the sine wave itself would be predicted directly from the phase of the frequency response (by dividing by the frequency of the sine-wave: with $\phi = angle(H(j\omega))$,  the time delay is $-\phi(\omega)/\omega$), while the time delay of the pulse envelope is predicted from the negative derivative of the phase with respect to frequency ($-d\phi(\omega)/d\omega$)).

These posts and answers are helpful:
Calculate the time delay introduced by group delay for IIR-Filters
https://electronics.stackexchange.com/questions/135475/physical-significance-of-group-delay
And most helpful to what otherwise seems like a paradox of causality for positive group delay is this paper https://www.researchgate.net/publication/253463703_Causality_and_Negative_Group_Delays_in_a_Simple_Bandpass_Amplifier referenced by Max in this post Physical Meaning of Negative Group Delay for causal LTI systems which I bottom line as causality is not violated but due to the bandwidth restrictions above we create a condition that causes the pulse envelope at the output to precede the input: The output pulse does not appear until the input amplitude varies (and if we have gain in the system the output envelope grows faster) and due to the bandwidth constraint and the result of destructive summation of the input pulse the output will start to decrease before the input does. Very cool DSP magic trick. See this post that illustrates this with a specific example.