You really do want to follow the lore in World of Warcraft, honestly. But sometimes the storytelling and the overall quality of the game makes that… well, difficult. Your eyes kind of glazed over partway through both Warlords of Draenor and Battle for Azeroth and you stopped reading the quest text. You definitely missed some patches in the original game. You still don’t remember what the heck was going on in Grizzly Hills in Wrath of the Lich King. What you need is the newly expanded and improved WoW Lore TLDR, a site with a single-spot summary of the game’s story stretching back through pre-history and into newer expansions.
The site has recently seen a major functionality and content update, adding a new layer of detail to expand as well as several more detailed summaries being added to older expansions. While the full-detail summary isn’t available for some of the more recent expansions, everything is at least summarized in broad strokes so you can catch up on the game’s story at a glance, along with having tooltips for important concepts like fel magic and world souls. Check out the site if you need a quick (or slightly longer) refresher on the story so far.