First off, It's going to depend where you are - paralegals have different licensing requirements in different jurisdictions.
Paralegals do a lot of different things. Generally speaking a paralegal can give legal assistance but not legal advice - however, in some jurisdictions (like mine) paralegals can also act as agents and represent parties in small claims court, on minor criminal offences, and in some quasi judicial tribunals. I've encountered paralegals who do collections work, specialize exclusively in traffic offences, etc. Others manage the more process oriented aspects in a larger law practice (though in my firm this is largely done by law clerks). Most paralegals can also act as notaries, commission documents, etc. (but it would, I think, be hard to make a living doing just that).