Could you settle an office dispute over whether the word “trainings” is legitimate? We might use it in a sentence such as “I have to go to three trainings today.”
I use the expressions training sessions, training modules, training classes, and training courses—not trainings—because, as far as I can remember, training has been an uncountable noun, like work, information, music, or air. I would tell my staff to avoid using trainings in formal contexts, such as in our training catalogue and company-wide training announcements.
But trainings has become a term of art in much of the business world, so it’s acceptable to many people, especially in informal emails. If it does not appear as acceptable usage in standard dictionaries today, it probably will in the future.