In flex material this is done where it is going to bend frequently.
Another situation for this is where the shielding effect is wanted but the capacitance needs to be reduced.
A further case is the Faraday Screen. By having long narrow conductors that do not form closed loops (like a comb with teeth and one connecting trace) there are fewer eddy currents caused by magnetic fields but the capacitive shielding is retained.
There are some situations where large PCBs bow due to differential strain caused when undergoing reflow or mostly when undergoing wave soldering. This usually happens under large amount of heat as you can imagine if one side of board has large copper area relative to other side, a bowing of board occurs when the PCB cools after wave soldering. This bowing may cause reliability problems later on, or could actually damage components etc.
Mostly hapens in large, double sided boards eg. have seen this problem in LED traffic light PCBs, with few traces on one side, but large ground plane on other side. Reducing copper material by meshing it also reduces effect of strain and PCB bowing when udergoing wave soldering. EMI etc are also very relevant. Meshing just because it looks pretty is silly ... RF currents prefer solid, low ESR/ESL ground planes.