What is the meaning of "age of energy into the age of matter" in the statement given below?
Our universe began to expand over 8 billion years age quickly passing from the "age of energy into the age of matter."
According to the "big bang theory," formation of the universe began with a huge explosion.
Prior to that explosion, scientists have not yet been able to construct a theory to attempt to explain the conditions, but there must have been an enormously concentrated energy source of some sort. This gigantic field of energy is the "age of energy" referred to in your quote - all that existed at that time was this centralized source and origin point of energy.
Immediately following the big bang explosion, the energy was expelled away from the centralized point with great force and speed. At the same time, the energy began to come together into subatomic particles - protons and neutrons - which began to join together to create atoms shortly thereafter. Over eons of time, these atoms joined to form elements, compounds, and matter - the gradual development that is referred to as "the age of matter."