Have you ever used Garmin back in the day, or a USB GPS receiver? It can take a minute or so to get enough initial information to deduce a location at a low datarate. AGPS gets some or all of that information (I'm not sure) from another source, usually a cell phone network so that first location is deduced much faster. Modern phones have GPS receivers, but use AGPS. If a modern phone has no network signal, it will still get a GPS signal, it will just take longer to get the first location.

Not to be confused with other technologies such as skyhook [2], which was used in iPhone 1 and other older devices to fuse radio signal strength, known wifi hotspot locations, etc as a kind of pseudo-GPS. It was only relevant for a few years.

Wikipedia [1] has a nice short explanation.

[1] https://en.wikipedia.org/wiki/Assisted_GNSS

[2] https://en.wikipedia.org/wiki/Skyhook_Wireless