Since you’re a programmer (yes!) I can use a few analogies. A transform is like a lossless conversion to another file format, or to another data structure (from a linked list to an array). Different formats have inherent advantages, so you convert to the representation that makes the most sense.
If you’re randomly inserting a bunch of elements, convert to a linked list and do the insertions. Later on, when you need random lookups, convert to an array. A math transform is basically that, converting data into a format which hopefully matches the problem domain.