First of all, I believe it should be "building block set".
A "building block set" is a children's toy. Search on google to see a picture. It's a bunch of small blocks that a child can use to build little structures. They stack them together to make buildings or robots or airplanes, or even people or monsters !
The paragraph you quoted is using this image of a "building block set" to describe nano-technology, but instead of little blocks of wood or plastic, you have VERY little nano-robots made of 90 atoms ! That is a very small robot !
To build something "from the bottom up" means that you are building it from the very basic level. The image probably comes from building a house, or an Egyptian pyramid. You can't build these things by starting at the top and working your way to the bottom. You must start from the bottom and work your way upwards. When someone says "I'm going to build this thing from the bottom up" they mean they are going to build the entire thing, from the very beginning to the very end. So if they were building a house they must start with the foundation, then the floor, then the walls, then the roof.
Nano-technology takes this concept to the extreme, because it REALLY goes to the bottom. You can't get much smaller than a block with only 90 atoms.