This is the first of what will be a significant number of questions we will answer over the course of the semester. Personally, I like this format; it lends itself to be able to expand statements a bit more broadly than in a more formal format. Besides, in this format, readership potentially is wide open if the author wanted that.
A strict definition of the word biochemistry, according to dictionary.com, is "the science dealing with the chemistry of living matter." The World English Dictionary further defines it as "the study of chemical compounds, reactions, etc., occurring in living organisms." If you consider both of these definitions in the context they are presented in, they are obviously (I think) both technically correct. But it can be considered in finer detail; most science doesn't occur in a vacuum, and to consider what biochemistry is, and why it is studied, it must be looked at in the context of other fields of study within the sciences. Specifically, its differences with other scientific disciplines need to be considered.
Comparisons are always difficult because any number of people will have differing views as to what something is or what it is not. In looking at differences between the disciplines I have found a considerable number of differing views as to what they are and what they are not. I've done my best to parse them out so that I could form my own understanding of the differences I'll talk about. So, here goes.
First, Biochemistry versus Biology: biology is concerned with the study of organisms, plants and animals alike. Biochemistry is the study of the chemical processes and reactions within those organisms the biologist studies.
Molecular Biology, on the other hand, is the study of cells within an organism. Both the structure of the cell as well as how the cell functions is the concern of the molecular biologist. This goes back to something taught in the first semester of general biology, a concept known as "The Central Dogma of Molecular Biology." I remember thinking, "there is a dogma to this?" But it's actually not a horrible concept; it is the manner in which sequences (RNA, DNA, and proteins, specifically) are copied, transcripted, and translated. How this differs from biochemistry is that molecular biologists are more interested how these processes occur but they are not concerned as much with the chemical underpinnings of the processes themselves. That is the domain of the biochemist.
The same can be said for the study of genetics; a geneticist's interest lies in how organisms differ, in terms of their genetic makeup - the ATGC's of DNA and AUGC's of RNA. Further, geneticists look at how those differences in genetic makeup affect survivability among organisms and the species they come from. A biochemist looks at how the amino acids and protein structure that make up DNA and RNA function properly.
In many ways the job of a biochemist can be compared to that of a software engineer who develops the low-level code for a given computer architecture - the firmware. Without firmware, computers won't operate. And software without hardware is an absurd concept if you think about it; I'm not suggesting that by using his analogy either biology or chemistry is absurd, but I am saying that without the study of biochemistry, our understanding of life, like the computer system without a base set of instructions to function, would be incomplete.