Daniel answered the programming side of things really well. To answer the other half of your question about whether it is a "real" word:
It is not strictly a programming word. Long before being used for programming it was used in other engineering disciplines. It meant literally attaching instruments (gauges, meters, etc.) to something to measure behavior or performance. Consider these excerpts from a NGram search:
"To date five modern submarines and three full-scale models have been instrumented in this manner." (talking about attaching gauges to the vessels to measure waterproofing) - 1955
One blade of each stiffness was instrumented to measure bending at nine spanwise stations - 1953
So the programming usage comes by way of an analogy. How do you measure the performance of software? You can't attach physical instruments to it, but you can use the things described in Daniel's link to look under the hood.