Is it possible someone could explain as if to a small child what data can be collected from GPS which shows this effect. I don't understand.
These distortions are not constant. They change from time to time. There are many different ways to account for them. One of the most accurate solution is to keep a GPS receiver on a well known location. Since you know that this receiver haven’t moved you can use the signal measured to estimate the parameters of the ionosphere between that station and the satelite.
Normally these signals are used to correct GPS navigational solutions. You take the closest station to your moving receiver and assume that whatever way the ionosphere was distorting for that station will do the same for your receiver too. This is valuable so there are network of such GPS stations in a lot of places.
Here they use the data collected by these stations differently. Instead of correcting a navigational solution they visualise the measured state of the ionosphere as seen by a bunch of these stations.