At the risk of sounding extremely ignorant, what does this entail?
If congress can't agree and come to a decision, the government does not have the authority to spend money on non-essential government funded things. Shut downs usually don't last long at all though.
What this means: all public services stay open (mail continues).
What stops: Obama will decide which government officials are important during the shutdown. The president and Congress will continue being paid. Lower-level government workers will not be paid. (Ex. NASA workers) In addition, military bills will not be sent out if the shutdown extends over a week.