The following list is mainly about Fallout 3 and 4 and contains spoilers for those games.

Anchorage
The city of Anchorage, in Alaska, was taken over by the Chinese in 2066 but was reclaimed by the United States in 2077. It then became a battleground and was reduced to ruins when the United States began its counter-invasion.

Brotherhood of Steel
The Brotherhood was founded by Roger Maxson, who was a captain in the US army. They are known for their vast collection of power armor and for regulating technology in the wasteland.

Commonwealth
The Commonwealth is a large body of land that encompasses the former state of Massachusetts. It is the setting for Fallout 4.

Dogmeat
Dogmeat is a follower that accompanies the lone wanderer in all Fallout games.

Enclave
The Enclave was founded after the great war by members of the pre-war government and military.  It is a secretive organization and is mostly comprised of descendants of government officials from the pre-war era.

Fawkes
Everyone's favorite super-mutant (other than Marcus), Fawkes, was a Vault 87 resident. He is friendly and is a possible companion of the Lone Wanderer.

Ghoul
Ghouls are necrotic post-war humans. Two branches of ghouls exist, feral and non-feral ghouls. They were mutated by intense amounts of radiation but have extremely long lifespans.

Holodisk
A storage device manufactured by Wattz Electronics. They can hold up to 256kb of data but some can hold up to 4000gb.

Institute
An advanced scientific organization based in the Commonwealth. They are known for producing synths.

Jefferson Memorial
The base of operations for the team of project purity, lead by James. Their goal was to produce purified water.

Kellogg
A skilled mercenary who was enlisted by the Institute to receive a cryogenically frozen human specimen from vault 111.

Liberty Prime
A one of a kind US army robot discovered in the depths of the Pentagon by the Brotherhood of Steel.

Megaton
A fortified settlement built inside a crater with an undetonated atomic bomb lying dormant in the center.

Nuka-Cola
Everyone's favorite drink produced by the Nuka-Cola Corporation. Their bottle caps are used as currency across the wasteland.

Overseer
The leader of a vault. Unlike most of the vault's residents, the overseer was aware of the vaults true (and usually evil) purpose.

Pipboy
A personal computer mounted on your wrist. They were produced by RobCo Industries before the war. 

Quantum Cola
Twice the calories, twice the taste of your standard Nuka-Cola. It has a peculiar blue glow.

RobCo Industries
One of the biggest computer and robotics companies in the US. They are known for creating the PipBoy and many robots that wander the wasteland.

S.P.E.C.I.A.L
The stats in all Fallout games. Strength, Perception, Endurance, Charisma, Intelligence, Agility and Luck.

Three Dog
Threeee Dawwwg!!! The greatest DJ in the Capital Wasteland. He is your host of Galaxy News Radio.

USS Constitution
A frigate built in 1797 that eventually had rocket engines strapped to it. It is now run by a crew of robots lead by Cap'n Ironsides.

Vault-Tec
A company hired by the US government to set up a vault system across the US to 'keep the residents of the United States safe'. I'm sure we all know their true purpose.

Wasteland
The world after the bombs fell was reduced to ash. It is now known as the Wasteland.

X-01 Power Armour
A variant of Power Armour still in the testing phases when the bombs fell. It is the greatest defensive suit of Power Armour available.

Yao Guai
A species of mutated black bear. They roam the Capital Wasteland and the Commonwealth waiting for its next meal.

Zetans
A species of extraterrestrials. Who knows where they came from? But they've been watching Earth for some time. It is thought that the Enclave's more impressive technology is based on that of the Zetans.