Bandwidth-delay product is also called bandwidth-time product, or BT, by analog filter designers.
A bandpass filter's bandwidth, B, is measured in Hertz, which are units of inverse seconds. A 4 kiloHertz wide bandpass filter has B = 4 x 10^3 Hz.
The group delay of a filter turns out to be roughly equal to the inverse of the delay time between an impulse at the filter input and the peak of the filter's impulse response at the output. (This is a good rule of thumb, but as with all rules of thumb, there are invariably some nuances that I'm glossing over.) So a qualitative understanding of the group delay of a filter is the amount of time it takes for a signal to pass through the filter. For example, a 4 kHz wide filter has a group delay of roughly 250 microseconds.
T refers to the symbol period of the signal passing through the filter. For example, a 5 kilobit per second binary phase shift keyed (BPSK) signal's symbol period is 200 microseconds, so that T = 200 microsec. Another example is a 5 kb/sec quaternary phase shift keyed (QPSK) signal. Since a QPSK signal transmits 2 bits per symbol, the symbol period is twice as long as for BPSK, so for QPSK, T = 400 microsec.
The BT product is used by radio systems engineers to specify filter bandwidths. In a radio system design, normally systems engineers specify the radio signalling speeds first (in bits/sec) before specifying filter bandwidths. Filter bandwidths should be designed as narrowly as possible without causing inter-symbol interference, or ISI. Generally, properly designed filters have BT products of between 0.8 and 1.1. When a BT product is greater than unity a filtered signal retains crisp leading and trailing edges of its symbols. When a BT product is less than unity ISI occurs. An oscilloscope snapshot of the output of the filter would show symbols beginning to blur together. This isn't bad in and of itself, providing the received signal level is sufficiently above the noise floor to demodulate properly, i.e., convert symbols back into bits.
In the examples above, we see that the filtered BPSK signal has a BT product of 0.8, i.e., ISI is beginning to become noticeable. The filtered QPSK signal has a BT product of 1.6. No ISI occurs through this filter, but the filter's bandwidth is probably too wide for a normally designed radio.
Variable data rate modems capable of transmitting multiple data rates require filters to have variable data rates as well. (Most telephone modems sold for dial-up Internet are adaptive-rate modems.) This is why much of the filtering is done by digital signal processors, which simulate the effect of analog filters in programmable digital hardware.