Biochemistry – Study of chemical substances and processes within living organisms
See this link to bio in biology.
Therefore, bio means "relating to life".
Biochemistry means life-chemistry or, more appropriately, the study of life or living organisms and chemistry.
Examples of biochemistry in a sentence
She studied biochemistry in college, she had always been interested in how living things work.
You need to know about biochemistry if you want to become a vet.
She was bored being a housewife, so she used her spare time to study biochemistry in the hopes of becoming a scientist.