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.