The first 12 values are the edge cubies, and the next eight are the corners. The faces are U(p), D(own), R(ight), L(eft), F(ront), and B(ack). First the cubie that's in the UF position is given, by the color (in UFRDBL notation) that's on top first, and then the other color next. And so on.
UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR represents the solved cube. Performing U, a 90° clockwise turn on the front face, would result in LF UR UB UL RF DR DB DL FU FD BR BL LFU URB UBL LDF RUF RFD DLB DBR.
Here are some visualizations that may be helpful:
That renders the input UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR.
The way the input works is by using the template of the solved cube. If DF was in the place of UF, then the orange-white edge would be in the place of the red-white edge.
If we were to swap, for example, the red-white edge and the red-blue edge, the visualization would look like this (with no changes to the hidden faces):
That renders the input UR UF UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR (which, btw, is an impossible cube state). Note that the order of the letters in cubies matter:
Above: UR UF UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR
Below: RU FU UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR
A cube scrambled with L2D2L2D2B2R2F2L2D2U2F2UF2U'R2UB2U'L2UB2U'LU'L2U'D'B2U'RBUBF'D' creates this visualization (only top, front, and right faces shown):
Solved: UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR
Scrambled: RU LF UB DR DL BL UL FU BD RF BR FD LDF LBD FUL RFD UFR RDB UBL RBU
As you can see in the comparison above and in the visualizations, the blue-red RU edge of the mixed cube is in the place of the red-white UF edge of the solved cube. The green-white LF edge is in the place of the red-blue UR edge, etc.