in general, DSP chip is a processor. it processes digital signals, such as digital audio stream, digital video signal and etc.
for example, there must be a DSP chip in a MP3 player, because the player needs a processor to calculate the digitally stored song in the memory, then output the calculated or processed song (in digital form) to DAC and subsequently convert the song to analog form, so that it can be amplified...
basic function of a DSP chip is to calculate calculate and calculate, hence it must have a very powerful core (such as ARM7 or ARM9) to do the calculation.
sometimes, it is really confusing, to differentiate DSP and MCU. in general, they are processors designed to process digital signal, but in terms application, DSPs are used for calculating digital audio or video signals where MUCs are used for controlling machines and etc.
hope you can understand!!!