Graphics are just video signals generated from data by a processing unit. This data comes from external memory and/or registers internal to the processing unit.
On the 2600, the TIA outputs playfield pixels in a loop. In parallel to that, each object (players, missiles and ball) has a counter that lasts one scanline, and when that counter expires, the object is drawn and the counter is reset, so the object is drawn at the same position every scanline. You position the objects by manually resetting these counters, and fine adjustments to the positions are made by clocking the counters additional times, forcing the objects to move specific numbers of pixels.
On the NES, the PPU is programmed to combine data from the name, attribute and pattern tables in a loop, using the scroll to calculate which parts of the name table to read. Background pixels are formed from that data and from the colors stored in palette RAM. Parallel to that, the PPU scans all 64 sprites in the OAM looking for the ones that will be visible on the next scanline, and it copies the graphics of the ones it finds to an internal buffer. While rendering scanlines, for each position the PPU selects either the computed background pixel or a buffered sprite pixel, taking the sprite priorities into consideration.
This is an oversimplification of the process, which is described in detail in our wiki
. There you can read about everything that the PPU does during each cycle of a frame.