Cell theory provides a very simple, succinct definition of life:
- All life forms are composed of one or more cells.
- Cells only arise from pre-existing cells.
- The cell is the smallest unit of life.
The major contributors to cell theory were Matthias J. Scheiden (often spelled Scheiden, Sheiden, Schlieden, etc, as the Germans weren't too picky about how they spelled their last names at the time) and Theodore Schwann, who coined the term. Scheiden came to the conclusion that all animals are composed of cells; Schwann took the next step and found that all plants were as well.
Of course, this is only considered a theory, and is highly likely to change in the future. The question of "where did the first cell come from?" (or DNA/RNA for that matter) is little more than a "chicken / egg" kind of question, and forms the basis of the scientific study of abiogenesis. It's obvious that there must be some sort of exception to the rule that "cells only arise from other cells," but this is how science works. When we observe the exception, we'll include it. Until then, this is the best we've got to work with, and it works for now.
The definition of life is still a subject of much debate, especially among those who consider viruses (either genetically composed, or digitally composed, or both) to be life forms. There are other more convoluted definitions of life that exclude cell theory in an attempt to include viruses (which are non-cellular chunks of pure genetic code and protein that manipulate other cells into making copies of themselves) among the living, but by using any combination of semantic trickery, one can easily argue that fire, water puddles, and the stars in the heavens are "alive" according to these rules (and perhaps, they are in some sense). At the very least, DNA/RNA viruses are generally accepted as "biological entitites."