Each level of a Structure or Unit adds one to your Logistics. As long as your total Logistics is equal to or lower than your maximum (as shown on The Assets - Overview page at the top) you're fine. However, for each point over you are, a 1% penalty is added to the upkeep of all your Structures or Units (depending on which Logistics os over).
For example, a level 5 Shipyard adds 5 to your Logistics and costs $1000 a turn in Upkeep. If your Logistics is 10 points over, your Shipyard costs 10% more - so $1100 per turn. This 10% fee is added to all your structures as long as you're over Logistics cap.