1. When one is doing certain numerical computations, an
approximate solution may be computed by any of several
heuristic methods, then refined to a final value. By using
the starting point of a first approximation of the answer, one
can write an algorithm that converges more quickly to the
correct result.

2. In jargon, a preface to any comment that indicates that the
comment is only approximately true. The remark "To a first
approximation, I feel good" might indicate that deeper
questioning would reveal that not all is perfect (e.g. a
nagging cough still remains after an illness).