How does a flip-flop circuit keep it state?
If we have a classical flip flop (like this image from wikipedia):



You can see that depending on the state this is in, there is constantly some current flowing (and "stealing" current through the R3/R4 path, thus shutting that one off). The result then is never changing again, as long as VCC is active, thus the state of the whole apparatus is static. If you switch off VCC, the data is gone, so "static" doesn't mean "runs without power" but "runs in a steady state".

On the other hand, for a typical DRAM cell (again wikipedia, sorry they did not have a single cell image):



One action fills one of the capacitors, but after a short time, due to leakage, the capacitor loses its charge. So you have some external circuitry that is constantly reading the bits (you can even see that they need a latching comparator there), and writing them again. Thus you have a lot of switching going on, the whole apparatus is dynamic. Not only needs it a constant power supply, but constant dynamic changes of its internal state.