I would say: just try the Google lookup of "define trainers" for yourself.
I did, and the first hit was http://dictionary.cambridge.or..., which gives as definition:
"a person who teaches skills to people or animals and prepares them for a job, activity, or sport:" and
"[ C usually plural ] (UK) (UK also training shoe, US sneaker) a type of light, comfortable shoe that can be worn for sport"
The second and third hit are directly for "trainers", not "trainer", and give
"A British slang word for Shoes." and
"plural noun / British / shoes that people wear, especially for running and other sports"
So, you are right that it is a British word, but not that a Google search for "define trainers" will not give you a definition.
I'm not a native English speaker myself, and I had no problem understanding the meaning.