Fixed duration and fixed units are terms that come from project scheduling software. The companion term is fixed work. Project scheduling software works on the general principle that duration = work * units. So if I have an estimated effort of four hours for a task and one resource (unit) to do the work, the duration is four hours. If someone works on that task 50% of the time, the duration is eight hours. If two people work on that task, then the duration is two hours.
Where the "fixed" part comes in is that when you are scheduling, you can instruct the software to keep one of the three variables fixed and make adjustments to the other two when re-calculating. So if I specify fixed duration, the work and the units may be changed, but not the duration.
Unfortunately the software is very flexible and does not openly support project management best practices as PMPs might practice them. To get the best result for your project, all estimates should be given in terms of effort (work) and your project tasks should be designated as fixed work.