The Spellplague was the third of the three great disasters to befall the Forgotten Realms, which served on a meta-level to justify the switch-up in mechanics and lore from one edition to the next. In this, it was the direct sequel to the Time of Troubles.
It is also, without a doubt, the most absolutely skubtastic aspect of Dungeons & Dragons 4th Edition, because of its massive - and unnecessary, in light of the more respectful treatments that 4e gave to Eberron and Dark Sun - adjustment to continents, metaphysics and characters. Whilst Faerun is infamous for having a particularly autistic fandom, the Spellplague didn't help by having a story that relied on way too many people either doing stupid shit or having more power than they should have just because the plot needed them to, with even fans who liked the basic idea agreeing that it could have benefited from a more competent backstory.
In a nutshell, as part of a long-running plan on his part, Cyric finally managed to arrange for the assassination of Mystra, one of his oldest enemies. Naturally, killing the Goddess of Magic did bad things to "The Weave", Toril's background magical fabric-thingy - it didn't help that Shar immediately tried to stick her hooks in it and claim it for herself. The result was that magic went completely haywire, causing magical spells and items across Toril to explode in surges of eerie blue flame that acted as magical radiation, complete with inducing bizarre physical and mystical mutations in anybody who was touched by the stuff and survived. Lots of people died, lots of shit got blown up real good.
Notably, Elminster saw most of his fellow Chosen of Mystra die and was himself stripped of 99% of his magical power, leaving him a sad and bitter man hiding in his burned-out tower and incapable of doing all the epic shit he used to do.
The Spellplague was ultimately cleared up when The Sundering occurred, pulling Abeir and Toril apart again and moving things on to 5th edition.
The effects of the Spellplague, and in particular the Spellscarred theme, are technically a kind of Wild Magic.