I took this information from the Nukeworker forum

ELT is an acronym for Engineering Laboratory Technician.  An ELT is an MM with additional training in boiler water chemistry control and analysis and reactor plant water chemistry control and analysis.   

A pressurized water reactor plant (the only type currently in use in the Navy) has two independent loops.  One loop circulates water through the nuclear reactor to transfer the heat generated by the nuclear reaction to a heat exchanger.  The other loop runs through the heat exchanger, turns to steam, and runs the steam turbines.  The loops are independent because the loop running through the nuclear reactor becomes radioactive.  (Of course, that's a simplified explanation, but it will do for now.)

Things in contact with water tend to corrode (rust).   (That's also simplified.)  So, to minimize corrosion, we add chemicals to the water.  We control the water in the reactor loop (called the primary loop) differently than the water in the steam plant loop (called the secondary loop).  One of the jobs of the ELT is to know what chemicals to add and to periodically monitor the water to determine whether or not to add more water or more chemicals to the plant.

I said that the water in the primary loop becomes radioactive.  Ideally, the water in the secondary loop is not radioactive.  Another job of an ELT is to perform radiochemical analyses to determine the level of radioactivity and what isotopes are causing the radioactivity in the primary loop, and also to test the secondary loop to ensure none of the radioactive water has leaked from the primary side to the secondary side.

The third job of the ELT is to monitor the radioactivity released by the nuclear reactor plant.  This is done in two ways.  First is to monitor the radiation produced by the reactor plant.  This is by using instruments such as a geiger counter.  The second is to monitor the contamination that might have escaped from the primary plant.  (Radiation is like the heat given off, contamination is like dirt or dust which is left when water evaporates.)  This is done in a similar fashion, but with a more sensitive instrument.

Typically, these tasks are performed exclusively by ELTs.  In the fleet, non-ELT MMs can by trained by ELTs to perform boiler water analyses, but as I remember, the ELT must add the chemicals.  The MMs do this because it is part of their watchstanding duties.  MMs can also perform radiation and contamination surveys, but usually do not because, with a few exceptions, the surveys are not part of their watchstanding duties.  Primary plant analyses are only performed by ELTs (with some exceptions, such as supervisory watchstation qualifications).

Nuclear ratings in my time were MMs, ETs, EMs, and ICs.  Prior to my time there were more ratings.  Currently, there are no more ICs  (Interior communication electricians) since the EMs and ICs did the same job.

An important part of nuclear qualifications is cross rate training.  So, everyone will learn the theory behind what an ELT does (what chemicals are used, what the water specifications are, what the radiation and contamination levels mean), but generally, only the ELT will perform those tasks.

Hope this helps.  More detail is available on request.

In reply to some other comments:

At times, prototypes have involuntarily assigned graduating MMs to ELT school.  In particular, I had one in my division who finished highly ranked in his class and had his heart set on being a welder.  (The two additional schools available to MMs who have successfully completed prototype training are ELT and Nuclear-grade welder.  These welders usually perform emergency repairs only.  Routine welding on both nuclear and non-nuclear systems is performed by the Hull Technician (HT) rating.)  So, some ELTs really would prefer to work as MMs most of the time.

I think I recall a case where a person was able to convince his detailer to get ELT school as his C school.

Some ELTs are picked up after prototype for staff instructor duty.  Also, some MMs who have completed staff instructor duty get ELT school before being sent to the fleet.