DTE : Data Terminal Equipment
DCE : Data Circuit-Terminating Equipment
The equipments connected on a serial link need to have exactly the same transmission speeds otherwise the link will flap (up, down, up, down, ...). However the internal clock of the equipments have probably not exactly the same speed (because they use quartz that are not perfect, these quartz use the local power frequency which wont be necessary the same, etc). As they don't have the same clock speed, they must find a way to be synchronized... The standards have defined that DCE will give the clocking to DTE.
Usually, DCE equipments are provider equipments (because they use the same clock for their entire network or at least for a great part) and DTE equipments are customer equipments.
I believe Christophe has covered the question nicely, so I'll just make a quick note that you can easily remember that the DCE provides clocking because its the only word with a 'C' in it, therefore dCe=Clocking