How do you increase 1 building power?

What determines '1' building power. Same with technology. I researched a technology and it seemed to count for 100 power.

Each upgrade on a building will have a power increase for it. Tap on any building and then on 'more information' to see the power level of it at each upgrade level. At low levels the increase will be 1 or 2 power, at high levels it will be hundreds or thousands of power.

What building? Any building can do like: banks, barracks, base, embassy, granary... Or do I need to buy the construction center.

Yes, well a few cannot be upgraded but almost all of them can. Tap on any building and tap the 'Details' icon that appears. Then if it can be upgraded tap the More information button. This will show you the levels and the power that the building has at each level.