“Exploit the constraint” comes from Dr. Eli Goldratt's book The Goal, where he identifies Five Focusing Steps as a way to continuously improve throughput.
The 2nd step is the focus on this blog post.
The premise is that when you encounter a problem you want to make it highly visible. The temptation for a lot of teams is to do the opposite and hide the problem as quickly as possible. For example, some teams experience broken builds on their nightly runs. Their immediate reaction may be to just run it once a week or disable it altogether. However, the correct course of action is to run the build more often (possibly hourly). This allows the team to test their potential fix quickly. It also provides them with some reassurance that the problem has been resolved.
Another example is adding memory to a high processing server instead of investigating what is actually causing the high usage.
In the book “Continuous Delivery” by Jez Humble & David Farley, they describe this technique as making the problem painful.
Essentially, once the root cause is clear only then can you permanently fix the problem.