You need to copy not only the mod files, but all the data files in to the relevant folders. I.e., in your unzipped mod folder, you may have mod.esp, readme.txt, datafiles
within data files there may be the folders textures, meshes and each could contain folders like a, n, w, x and each of those in turn will contain the data files relevant to the mod. You need to copy the files only into the same directories within the morrowind data files (just the files, do not copy folders into folders).
After that you need to open the morrowind.ini file in a text editor, this file just contains a load of preferences for the game. Scroll to the bottom and then a few lines up there should be some lines saying:
[Game Files]
GameFile0=Morrowind.esm
GameFile1=Tribunal.esm
GameFile2=Bloodmoon.esm
Add to the bottom of this the name of your mod, e.g.
[Game Files]
GameFile0=Morrowind.esm
GameFile1=Tribunal.esm
GameFile2=Bloodmoon.esm
GameFile3=Morrowind Patch 1.6.5 Beta (BTB Edit).esm
Ignore the .bsa files as far as I know. Perhaps some mods include one of these?
Save, then it should run.
Note however, that somewhere on you computer, possibly under application support, a copy of this file is made which must be deleted for the edited version to take effect. You will have to do you own research on this. I have got the unofficial patch loading on my macbook, and am about to try out a payload of other mods.