White Dwarf is a monthly magazine from Games Workshop which has quite frankly gone to the fucking dogs. The name is a reference to both fantasy dwarves and white dwarf stars, as the magazine's original tagline was "The Science Fiction and Fantasy Games Magazine." Later they created a mascot, Grombrindal the White Dwarf, a dwarf with a white beard.
The Old Times
In the beginning, it was just a rubbish magazine from London that advertised whatever games GW had the rights to publish in the UK, including Dungeons & Dragons (several monsters were actually born out of White Dwarf's "Fiend Factory" article, where fans submitted new monsters - this is where the Githyanki came from), Traveller, and RuneQuest. When they produced their own game, Warhammer, it became a primary focus of their magazine. Issue 93 (from 1987) is a big one in /tg/ history, because that's when they announced Warhammer 40,000: Rogue Trader.
The halcyon days were around 1998-99, when 3rd edition 40k was shiny and new and Adrian 'WAAAAAAGH' Wood worked there on a reasonably frequent basis. The general level of grimdark was pretty low and they even included battle reports for the good specialty games as and when they got released, most notably Mordheim and Battlefleet Gothic. Oh and they used to actually put army lists before all of their battle reports, and gave the actual turn-by-turn play. They stopped doing the former because people with calculators were able to backwards engineer army lists from them and thus not buy codices (luckily the internet came along, making buying anything that can be stored in a PDF strictly optional), and they stopped the latter because it meant that their flavor-of-the-month army could get humiliated. Sales fell from here. It was a depressing time for Games Workshop.
White Dwarf also used to have a Chapter Approved column with experimental rules and errata. The errata went away when GW realized that they could put errata online and use the saved space for more advertisements, and by the time the experimental rules became actual rules, GW was no longer doing playtesting in public.
Anyway, White Dwarf is alright, but no where near as awesome as it once was. The real point of decline was when it started shilling for the Lord of the Rings game that no-one ever played.
In 2012, GW re-released it. It became a decent magazine, but not worth ten dollars.
We weekly now boys
In January 2014, it became known that Games Workshop would reinvent White Dwarf again in February. White Dwarf was announced to became a $4, 32-page weekly magazine which would focus on the hobby, featuring, for example, model and book releases, rules updates, and modeling features. Games Workshop would also release a monthly 236-page "Warhammer Visions" magazine at $12, which would also be available for iPad. GW would convert all remaining White Dwarf subscriptions to this "Warhammer Visions" magazine. This magazine would focus on wider hobby news, Citadel model painting examples, various articles to deal with conversions, etc.
Back to monthly
In late 2016, WD went back to the monthly model. Warhammer Visions died, but now we got a new magazine with batreps, painting tutorials, news, joke segments, and most oddly, FREE SHIT. Issue one came with a fucking SLAUGHTERPRIEST for FREE. A model that costs £7 more then the goddammed mag.
In 2019 the magazine got a soft reboot, becoming more like the older times: it contains new short stories for both 40k and Age of Sigmar, the return of Index Astartes (plus Index Imperialis/Xenos/Whatever) featuring stuff like additional rules and stratagems for lesser Space Marine Chapters or updated Index profiles for smaller armies like Ynnari, Assassins and Inquisition, an equivalent for Age of Sigmar called The Tome Celestial which gives additional stuff for some subfactions of various armies like some new Warscroll Battalions or new named character variations of generic heroes, more new rules for games (such as new battleplans for both 40k and AoS, new Kill Team armies and models, additional quests for Blackstone Fortress and side game variants of Warhammer Underworlds), more columns and articles about modelling or game strategy and stuff. And, most important, no direct promotion of new models whatsoever, the most you may see are some articles tying in to recent releases or casually mentioning/showing new books or models in a "You should already know that this exists" way.
In 2020, due to the Covid-19 lockdown, White Dwarf issues got the kinda hilarious penchant to keep promoting stuff that isn't out yet as if they were out, such as the May issue (which ended up being released in late June) saying "Hey, want to try the new Lumineth Realm-Lords in Warcry? Go and buy a box of the basic troop guys!" except that the basic troop guys aren't going to be released outside of the limited release big box before September.
Dungeons & Dragons was one of the first game systems to be covered in White Dwarf, back in the days before Warhammer Fantasy. There were quite a few articles, and you can check out the list here: http://wiki.oldhammer.org.uk/v/Dungeons_and_Dragons/White_Dwarf_Index