Short answers, pulled from the story.
Jugurtha was the nephew and adopted son of King Micipsa of Numidia, adopted as a potential heir alongside Micipsa's sons Adherbal and Hiempsal I. He became sole king by having Hiempsal assassinated, defeating and eventually executing Adherbal, and bribing Roman officials to overlook his actions.
The Jugurthine War was fought from 111 to 105 BC between the Roman Republic and King Jugurtha of Numidia. The kingdom itself did not become a Roman province until 46 BC.
Rome declared war on Jugurtha in 111 BC after he besieged and executed his cousin Adherbal, a Roman ally, along with the Romans who had helped defend Adherbal's capital, Cirta. Public outrage at the killing of Roman citizens, pressed by the tribune Gaius Memmius, forced the Senate's hand.
The war ended when Gaius Marius's quaestor, Lucius Cornelius Sulla, negotiated with King Bocchus I of Mauretania, Jugurtha's father-in-law, to hand Jugurtha over as a political hostage. Bocchus's men massacred Jugurtha's remaining followers and delivered him in chains to Sulla; Jugurtha was later executed in Rome after appearing in Marius's triumph in 104 BC.
Gaius Marius served as an officer under Quintus Metellus before winning the consulship for 107 BC and taking over command of the war through a law passed by the Tribal Assembly. He waived Rome's property requirement to recruit the poor Capite Censi into the legions, campaigned through Numidia, and ultimately secured Jugurtha's surrender via Sulla.
The war showed how thoroughly bribery could compromise Roman senators, commissioners, generals, and tribunes, since Jugurtha repeatedly bought his way out of accountability. The historian Sallust wrote a monograph on the war, Bellum Jugurthinum, treating it as an early marker of the ethical decline that he believed led to the eventual fall of the Roman Republic.