What is a Logic Library?

The link provided is to do with chip fabrication, so the art involved is more complex because a substrate is being doped with different chemicals which could bleed over into other parts of the substrate.  Take screen-printing as an analogous process - look at the corn flakes packet at breakfast and note the simple "clunky" design of colours on the box - if there is a misregistration of the different colours on the box due to tolerances in the way the cardboard is fed through the machine then it doesn't affect the design in a way that will cause the output to be scrapped.  This is "by design" to maximise yield.  A chip can be doped with different chemicals using a similar process.  Obviously the tolerances are extremely fine.  

All logic functions can be done using just the one logic function - the 2-input Not And gate (NAND gate), daisy chain enough of these in a particular way and virtually anything can be built using them - this is the building block of the high tech world, and this would also be a building block in a logic library.  However these will take up more space than is available, particularly as the border round an embedded device such as this needs to be electrically dead to avoid leakage across the surface of the substrate, so chip designers have come up with ways to combine lots of these gates together in optimal ways to create whole sub-systems, such as a Central Processing Unit (CPU) which manages the fetching of data from outside the chip, performing operations on that data, then putting it back to another location outside the chip.  Rather than everyone re-inventing the wheel these designs are made available to other designers.