Actually....

In every other application and API I have ever used, Y is ALWAYS the up/down axis, and Z is the depth axis. This is because x and y have always been the screen coordinates (since back in the early days of 2d graphics). When coming into 3d, a new axis was needed, Z , using a depth buffer, or ZBuffer (depth into the screen)

Well, Blender has flipped everything 90 degrees. To make it easier to understand, think of x and y as "ground" coordinates, with Z as a height coordinate.

Or better yet, don't think about any of that stuff and always remember than when importing or exporting anything to/from Blender, you have to rotate it 90 degrees  : /

This is why most every good importer/exporter for Blender has a "Z-up / Y-up" type of option.