Fate has multiple timelines to follow but the general plot of each timeline goes like this:
The Holy Grail War
A secret battle royale between 7 Mages (Masters). They fight for the Holy Grail, a magical cup that grants any wish.
In the Story Masters can summon Heroic Spirits/Servants (historical/mythical legends) to fight for them.
The summoned figure can be a historical figure or a person from a widely known story.
Historical Heroic Spirit example is Miyamoto Musashi or Nikola Tesla.
A Heroic Spirit from a widely known story (arguable) is Arthur Pendragon.
Btw difference between Heroic Spirits and Servants are:
Heroic Spirit is the whole version of the person, with access to all his/her knowledge, skills and weapons in his/her whole life.
Servants are copies taken from Heroic Spirits at a specific point of their life and given a class.
Example, one of the most famous Servants is Gilgamesh, widely known for his Archer Class where his main technique of attacking is summoning swords and flinging it at opponents, but he also has a Caster Class.
This Caster Gilgamesh is an older and wiser version. Instead of firing swords, he uses magical attacks.
They're the same person but at different points of their lives.
Fate sometimes gender bends these characters, like Miyamoto Musashi is a woman in here, or in another timeline Arthur Pendragon is a woman named Artoria Pendragon.
They can also have a different name but still be a historical figure like Iskandar, he is Alexander the Great.
Servants are categorized into 7 classes:
Saber, Archer, Lancer. Rider, Caster, Assassin, Berserker. (Like RPG classes Assassin, Mages, Archers,etc...)
The classes are very easy to understand:
Saber = Swords/Close to Sword
Archer = Bow/Projectiles
Lancer = Spears/Lancer/Long Melee Weapons
Caster = Magic/Any Voodoo Stuff
Rider = Mounts/Animals or with wheels
Assassin = Sneaky/Daggers/Assassination
Berserker = Caveman angry, Caveman strong/Insane
There are other classes that Servants can have in special circumstances. (They're gonna be explained in the story when they happen anyway so don't worry if there even is one in the story)
Noble Phantasms (NP)
A Servant's ultimate weapon or ability (e.g., King Arthur's Excalibur). It is powerful but drains mana and reveals their secret identity.
Command Spells
Three red sigils on a Master's hand. Using one forces a Servant to obey an absolute order. Each use consumes one command spell.