Biochemistry was the study of chemical processes that occurred in lifeforms. It could also refer to the biochemical makeup of these lifeforms as well.
In 2269, Harcourt Mudd sold love potion crystals to the inhabitants of Sirius IX, which made them all ill. Mudd had not counted on their unusual biochemistry before selling it to them. (TAS: "Mudd's Passion")
Tom Paris took two semesters of biochemistry in the Academy. This qualified him to be a field medic on board the USS Voyager. The biochemistry course Paris enrolled in did not teach how to perform a respiratory series. (VOY: "Parallax", "Phage")
Later that year, The Doctor examined Tuvix in Voyager's sickbay and discovered he was the result of a transporter accident that merged Neelix, Tuvok, and an orchid together. While scanning Tuvix, The Doctor found that the orchid was a part of Tuvix's genetic structure but it was not affecting his biochemistry. (VOY: "Tuvix")
In 2373, The Doctor told Kathryn Janeway that the sub-dermal bio-probe he placed in her would pick up any changes in her biochemistry when she went into the Nechani sanctuary to try to save Kes' life. Later, The Doctor observed Janeway's life signs in sickbay and found that her biochemistry was undergoing a unique series of interactions, meaning that she was under an hallucinogenic effect. (VOY: "Sacred Ground")
Later that year, Kes attempted to save Tieran's life by giving him twenty milligrams of lectrazine. It was ineffective in reviving his heart, since the medication was incompatible with his biochemistry. (VOY: "Warlord")
In 2377, B'Elanna Torres apologized to The Doctor after tampering with his program to make him remove all Klingon DNA from her unborn child. The Doctor told her she "was not guilty, by reason of biochemistry." (VOY: "Lineage")