It's a general term for doing something to your code necessary for some further analysis.
Especially for languages like C or C++, there are tools like Purify or Quantify that profile memory usage, performance statistics, and the like. To make those profiling programs work correctly, an "instrumenting" step is necessary to insert the counters, array-boundary checks, etc that is used by the profiling programs. Note that in the Purify/Quantify scenario, the instrumentation is done automatically as a post-compilation step (actually, it's an added step to the linking process) and you don't touch your source code.
Some of that is less necessary with dynamic or VM code (i.e. profiling tools like OptimizeIt are available for Java that does a lot of what Quantify does, but no special linking is required) but that doesn't negate the concept.