Nuclear Field "A" School was a tremendously formative experience. Details regarding the Machinist Mate rating can be found here.
Basically, the training is similar to "conventional" Machinist Mates with some additional heat transfer and fluid flow and if I remember correctly some foundational electrical theory and math courses.
It started with learning about the tools required to do basic repair (everything from screwdrivers to torque wrenches), progressing through precision measurement tools and techniques (vernier calipers, laser shaft alignment).
Mechanical theory was the next step. Learning essential components, construction and operation of valves, pumps, compressors, condensers, boilers, pneumatic, water purification, hydraulic, and air conditioning/refrigeration systems.
Practical Training followed with labs in heat transfer and fluid flow, open and closed loop systems, pumps, air compressors, oil purification , and valves. This is where we had the opportunity to operate, troubleshoot and repair the systems we had learned about using our newly attained knowledge. I fondly remember disassembling and reassembling pumps, valves, several kinds of oil purifiers and and 5-stage air compressor. I learned how to insulate piping systems, lap high pressure steam valve seats, repack valve stems and tweak control systems.
I have always liked tearing things apart to see how they worked so I really enjoyed this. The difference in this case is I had a fundamental understanding of what I was actually doing and was doing it with the right tools, usually with drawings of whatever it was I was working on. This was set up very similar to a college chemistry or physics lab... except instead of chemicals and oscilloscopes... we had a playground of operable pumps, valves, and purifiers.
One of the most fascinating thing about the Nuclear Field in the Navy is the selection process to each of the three ratings (Electronics, Electricians, Machinists). The Nuclear Navy had been doing this training for a number of years at the point I started (since sometime around 1945 - 45 years or so) and they had apparently learned a lot of things about people. There is a test that every potential nuclear operator takes prior to entry into the military called the Nuclear Field Qualification Test (NFQT). The scores on this test coupled with the specific strengths and weaknesses on the Armed Services Vocational Aptitude Battery (ASVAB) test apparently tell them which category you best fit. Person to person it was amazing how well they fit into each area.
My takeaways were a greater knowledge and respect for the details associated with mechanical components in general and specifically within propulsion plants and support systems.