The expressions (not equations!) you're referring to are part of how you implement a 2D array using a 1D array.
Say you have a 100x200 texture stored as a 1D array of 20000 texels (as opposed to 100 separate arrays of 200 texels, which would be terrible). If you want to get texel (50,30), then assuming the texels are stored in row major format, that means we want element (50*200)+29 of the array. In other words, (j*width)+i. Then there's a *4 because the array elements are all 4 bytes large.
The tileNumber % (m_tileset.getSize().x / tileSize.x); is doing something similar, though it's assuming the texture is broken up into tiles and trying to get the coordinates of one corner of a given tile, rather than a single texel.
Keep in mind that there are two sets of coordinates involved here: the x/y coordinates where we want to draw the tile, and the u/v coordinates where the tile is located in the tilemap.
I probably made a few silly mistakes but that should at least get the idea across.