The word "federation" comes from the Latin words foedus ("covenant", "pact", or "treaty") and the Late Latin word Foederatio ("a league or treaty").  It was borrowed from French (fédération) and entered English in the early 18th century, originally meaning "a union by agreement". This etymology highlights the core concept of a federation as a union of states or groups that have entered into a treaty or covenant with each other. 

According to the Oxford English Dictionary (OED), the earliest known use of the noun federation in English is from 1652 when the word was used in the Racovian Catechisme. 

Examples of "federation" used in a sentence: 
"The United States is a federation; the states all fall under the same federal government."
"He had been a member of the Social Democratic Federation since 1883." 
"In 1889 an important step towards federation was taken by Sir Henry Parkes." 
"Confalonieri, who was in favor of an Italian federation composed lEngelsm of northern Italy under the house of Savoy, central bardy." 
"Since federation no chartered bank has been compelled to liquidate without paying its note-holders in full." 
"Out of this grew the Free Church Federation, which secures a measure of co-operation between the Protestant Evangelical churches throughout England."