I'm fairly new at Microsoft SQL. I've seen many tutorials online on how to add a file to the database. What I still don't get is why?
There's several reasons one could and should do this. One of the less discussed items is logical file contention within the MDF/NDF file. When you have a lot of processes trying to access data in that single file it becomes a logical point of contention which will add lots of PAGE_LATCH wait times (not page_latch_io which is physical contention). See here for more info.
As your database grows you might want to spread the files to different drives for expandability. Of course, SQL Server uses a round robin proportional fill algorithem so you'd have to be mindful that it will create a hot-spot until it's the same size as the others. You can read more info on that in BoL here.
Other old school reasons used to be to separate indexes so you improve writes. This has largely gone to the wayside due to flash storage and intelligent SANs but if you need to squeeze every last bit of write IOPS out of it, then this would help. Basically optimization.
Sometime's it's helpful to move data from old disks to new disks or if the old disks are showing bad sectors or such.
Those are some of the main reasons someone would add different files. The main reason I do it is to avoid logical file contention however in many environments I've worked in now that SSDs and cheap RAM are so readily available, personall.