What is this?
This is what is called a shabty. They were buried with an individual to help with work in the afterlife, almost like servants.
Why are their hands around their chest?
This pose indicates that they represent the dead and served to identify them with the god Osiris, the king of the afterlife. The is referred to by Egyptologists as mummiform--mummy shaped--or, especially in the case of a king, Osiride--Osiris-like.
Shabties like these would be placed in the tomb. They're essentially servants to the deceased, who would perform tasks like farming for them in the afterlife.
Any idea what material makes this blue?
Yes! This is made of faience, a material made of a quartz based paste that could be molded and fired to create small sculptures like this. The ancient egyptians added a copper compound to the paste to create the blue color.
How was it preserved so well to retain its color?
Faience is fired like clay, and then glazed. It is a very stable material!
Tell me more.
These figurines were inscribed to the person they were buried with and were thought to come to life in order to help with chores, especially agricultural tasks.
They came in a wide range of qualities, from customized and individualized (the most expensive) to mold made and mass produced.