The latter two relate to the adjacency system.  The neighbour effect means that it will give +1 level to manufacturing improvements built in hexes next to that improvement.  The +5% is per level. 

For example, if you had two basic factories next to each other they would give +1 level to each other, which would me they would be getting a 5% bonus each.  So both would give +20% to manufacturing. If you build them separately they just produce +15% each.

If you were to put three in a line the outer two would get +1 level, while the middle will get +2.  So the outer factories produce +20%, while the inner would give +25% (15% + 5% + 5%).  Build them in a triangle formation touching and everyone will get +2 (+10% bonus), etc.

This work for the other types of improvements as well (research, wealth, military).  The bonus may vary depending on the building.  For example there are manufacturing improvements where the bonus is to raw production and not to colony manufacturing.  Then there are the hyperion buildings that can give bonuses to fleet logistics and mass capacity of ships.