A method to find the best solution when there are linear equations and/or inequalities.
Example: on this graph we see three different restrictions, and we can find that the maximum value of y 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.