They love fixing things, even if it isn't broken. They were conscripted into the Covenant against their will but were later freed by the Humans and the Elites. Their tentacles can split off into tiny cilia to disassemble components and reassemble them in seconds, often with intense modifications over the original components. This is how Johnny's shields and armour were improved massively over every other Spartan, thanks to a chance encounter with an Engineer in the Truth and Reconciliation.
The Covenant realised that the Engineers were peaceful and for some reason hated them for it. They therefore decided to strap Engineers with bombs and shield projectors to aid the Covenant Army. The Engineers would then shield their allies whilst destroying themselves to kill enemies, which was seen as cruelty by the Engineer-friendly members of the Covenant. This meant that use of this strategy was banned by most Covenant... except Brutes.
The Engineers decided to side with the Humans after resentment towards the Covenant turned to outright hatred. The Engineers sided with the Humans and provided vital information about Covenant tactics, troop deployments and technology. The UNSC Infinity had a sizeable population of Engineers aboard even after the Human-Covenant War. Since they have no homeworld, the Humans agreed to share Earth with the Engineers, who then spread out across the Galaxy from there. Now commonly regarded as the best mechanics in the Galaxy, few planets in League space go without at least a small Engineer population to aid in technological advancement.