The universe is so large and so old, that the numbers are nearly impossible to fathom. A comparison that can help put some perspective on the age of the universe is to compare the 13.7 billion year age of the universe to a calendar year on Earth. By this comparison, the universe began on January 1st, and by May, our galaxy, the Milky Way, had formed. Our Solar System formed in August, and by September, the first life had formed on Earth. Complex life such as fish, amphibians, dinosaurs and mammals formed in mid December, and all of human evolution took place during the last minutes of December 31st.
Image credit: Eric Fisk
This video from Khan Academy gives some comparison and perspective on the size of the universe: