Assisted GPS (A-GPS) can refer to a few different things.
It can be using nearby mobile phone cells or wifi networks to figure out the approx location.
Or it can be downloading the satellite almanac, over wifi or the phone connection.
Maybe also setting the time accurately (using NTP).
It usually helps a lot, much quicker for finding your position. Especially for phones/tablets, most of them seem to have poor GPS receivers. Though A-GPS will probably use a bit of data, so you might not want to use it if on a metered phone connection.
It can also give an approx location if indoors.
A-GPS won't actually help much with overall accuracy (assuming you are outside, and have a good view of the satellites).
Most of the Etrex models let you say you have moved a long way. Usually by going to the satellite screen, then press menu, then "New location". Then you can pick your approx location from a map. Don't know if this works on the Etrex 20/30?