Take a concrete example. Let's assume that I have a recording in PCM at 44.1kHz, and I want to see all of the frequencies present, to a resolution of 10Hz. Nyquist tells us that we only have 22.05kHz of signal present in the sample (well, one can hope, otherwise if the recording didn't filter out everything above that when coding to PCM, we're going to have a mess of aliasing going on, which is outside the scope of this post - just assume the person doing the encoding knew what they were doing, mkay...). So, 22.05kHz. And we want a resolution of 10Hz, so we're going to need 22.05kHz / 10Hz = 2205 samples. Of course, we actually need double that in the time domain (we throw away the phase information remember), so we need 4410 samples in the time domain to get our 2205 samples in the frequency domain. 4410 samples at 44.1kHz sampling is equal to 0.1 seconds.
If I decide that I want a better frequency resolution, say down to 1Hz, then you quickly arrive at the conclusion that you will need a full second of samples. In other words, your resolution in the time domain has decreased as you improve the resolution in the frequency domain.
You can improve a bit on this situation by using a sliding window with a carefully chosen windowing function. The frequency information will still be smeared out in time, but the windowing function reduces the amplitude of a frequency the further it is from the centre of the sampling window, which sharpens up the smear a bit.