Fate is a series about Holy Grail Wars and the summoning of servants to have a wish fulfilled. However Fate/Extella is a spinoff of that which originates from a PSP game called Fate/Extra. Servants are summoned by masters and they serve them by fighting to win the Holy Grail War. This isn't how the plot of Fate/Extella works but that's the original concept. Each servant is usually a historical or mythological person of some kind. Basically someone that is remembered by the masses, they can be fictional (e.g. in theory Zeus could be summoned). Masters are given command seals which they can use to control their servant, they are given 3 absolute orders which can be given to them (Fate/Extella gives you these back every map). However the strength of the command is based upon how specific the command is, something vague like "always do exactly what I tell you to" doesn't have much value and would just be an annoyance for most servants, they would be able to resist the command. Each servant hides their identity since if the enemy finds out who they are, they could research their weakness, how they died, etc which puts them at quite the disadvantage. As such servants are usually referred to by the class they are summoned into (Saber, Archer, Lancer, Caster, Rider, Assassin, Berserker). In some cases servants don't even trust their master with their true identity. Each servant has a Noble Phantasm, think of it as their strongest attack, however they are reluctant to use it since most of these attacks are unique, meaning if they use them and do not kill their target or someone else sees, then one could track them down and discover their identity. That's the gist of Fate, not all Fate/Extella related however.