A method to find the best solution when there are linear equations / inequalities.
Example: on this graph we see several restrictions, and we can find that the maximum value of y within them is about 2.1 (when x is around 1.1)
"Planning" is maybe a better word than "programming" (which was chosen before computer programming was common).
Very useful in industry for finding the best level of production when faced with varying costs, manpower, sales levels, etc.