over = so as to rest on or cover; on or upon: (from dictionary.com)
e.g. (look at this sentence)
Throw a sheet over the bed.
I think we lay a sheet over the bed. We actually don't throw. So, does in this sentence the `throw' mean `lay'?
'Throw' is more violently physical than 'lay'. Compare: Don't throw your book on the table!-- Lay it there.
I've heard it used to mean something done in a rushed manner or carelessly.
"As soon as I throw some dinner together for the kids, we can leave."
"Throw on some clothes and come for a walk with me!"
[native speaker, US, not teacher]