Well, everyone has already answered your specific question. I will try to give a more complete answer so that you know what you can find in it (not only "means this").
DMG stands for Dungeon Master Guide, one of the main books of the D & D system, which helps DMs in their work, describes how to execute your adventure, how to create your own things (cities, monsters, magical objects) and offers some additional optional rules. as a guide, for example, flanking rules and injury rules (lost members, etc.), which are not predetermined in the game.
As a player, probably the only part of that book you should know about is the Magic Objects section, so you know what magical elements they give you.
If you have more questions about the abbreviations, the Adventurer League Frequently Asked Questions (which can be found here, although I recommend downloading the Players Pack that has the updated FAQs, the main page is season 6 as of 11/21/2018) provides a good list of common abbreviations for the names of books. I copy it here, but it is updated as new books are published, so you know where to look when you need it.
- PHB. Player's manual
- PBR. Basic rules of the player
- DMBR. Basic rules of Dungeon Master
- DMG Dungeon Master Guide
- Mm. Monster manual
- EEPC. Elemental Evil Player Guide
- SCAG. Adventurous guide of the coast of the sword
- VGM. Volo's guide to monsters
- XGE The Xanathar guide for everything
- TP "Tortle Package"
- ALABAMA. League of adventurers
- ALPG. Adventurers league players guide
- ALDMG League of Adventurers DMG
- ToD. Tyranny of the dragons (Season 1)
- HDQ. Hoard of the Dragon Queen (Season 1)
- Putrefaction. Rise of Tiamat (Season 1)
- USA Elemental Evil (Season 2)
- PotA. Princes of the Apocalypse (Season 2)
- Bar. Rage of Demons (Season 3)
- OotA. Out of the abyss (Season 3)
- CoS. Curse of Strahd (Season 4)
- SKT. Thunder of the Storm King (Season 5)
- KIND. Tales from the yawn portal (Season 6)
- ToA. Tomb of annihilation (Season 7)