As far as ship engineering goes (I've no idea about on foot engineering), a blueprint is an engineering modification, such as increased FSD jump range, or an overcharged or lightweight weapon. You can pin one of these blueprints per engineer. By pinning the blueprint, you are then able to implement that modification using remote engineering, meaning you don't have to actually go to the engineer to do it but can do it when docked at any station.
If you do this, make sure that you have the necessary reputation with the engineer first as you will only be able to improve a module up to the level that your reputation with them allows and remote engineering does not increase your reputation with an engineer whereas if you modify a module at an engineer your reputation with that engineer increases. Also note that while you can run all the engineering rolls you cannot add a special effect remotely, for that you have to visit an engineer that provides that engineering blueprint, although that needn't be the engineer from who you pinned the blueprint.
Reputation is your standing with a faction, and influence is that factions influence in a system. The better your reputation the better the missions and mission rewards you will be offered. You'd try and improve a factions influence if you wanted to help them take control of assets in a system.
Hope that helps and it's the info you are looking for. Can be a bit confusing...
