When we require that a frequency-dependent block (filter) should only delay any signal by the time T - without changing the form of the signal the output-to-input relation is:
Applying the LAPLACE transformation to this equation the ratio (transfer function) is:
That means: (1) Magnitude |H(w)|=1 and (2) phase function phi(w)=-wT.
Hence, we require a phase function that is a LINEAR function of the frequency.
Definition: The group delay D is defined as D=-d(phi)/d(w). We see that for a linear phase function the group delay is D=constant.
However, it is to be mentioned that a real lowpass can never realize a transfer function H(s)=exp(-sT). Hence, we need an approximation "as good as possible" within a limited frequency band. This requirement leads to the well-known Thomson-Bessel approximation.
In most cases, the cut-off frequency for a Bessel filter is defined in the time domain (and NOT in the frequency domain, as it is normal for all other filter types). The cut-off (end of the passband) is defined at a frequency where the deviation of the (nearly constant) group delay D has a certain percentage of the value for low frequencies - depending on the particular application.
Remember: The BUTTERWORTH approximation has a "maximally flat magnitude" within the passband - the BESSEL approximation is derived from a "maximally flat group delay" requirement.