Overflow Servers are an opportunity to "double" or even "triple" dip on gathering materials.
For example, you can go to the Strawberry farming spot that I showed
you already, enter an overflow server, and then gather all the
Strawberry nodes again! Log out of the game, log back in, and then
accept an overflow server if given the opportunity. Once more, the
Strawberry nodes (should almost always) be back again for your picking
Enjoy! This strategy will only work while so many players are in the
starting zones, and maybe possibly again when everyone is playing level
80 end game areas.
Without this method, you'd be stuck waiting 23 hours for the Strawberries to respawn.
Obviously, you can't always assume that you will get an overflow server option. This only happens if there are too many players in your world and the game decides to offer you the option to avoid latency issues and/or stress on the system. What you can do however is start your gaming session by warping from waypoint to waypoint gathering resource nodes. Then at any moment if you get the overflow server option you can punch your ticket and refresh all the previously farmed areas.