What's the general difference in a in-depth explanation? Typically I would use local scripts, for no apparent reason but now that I think, I do not understand the differences between the two and what sections the type of script should be implemented into.
Basically local scripts are used for making things only happen for one player, usually used for guis. Server scripts happen for everyone. For example, if you make yourself green in a local script, nobody else will see it. Likewise, if you used a server script to make everyone green, everyone would see it and be green.