What is Law?Edit
Most academic law courses begin with this sort of a question.
Start now by trying it: Write down as many characterstics of law as you can think of.
If you have other people around, ask them. See how your lists compare.
I'd suggest some of the words you might have used would be:
- Enforcement / enforceable
- Authority (as in, rules created by an accepted authority)
- State / Government
Implicitly here I am assuming we are talking about the law of a state (in the sense of an international country, rather than a domestic unit - i.e. I mean the USA, not California).
This is not the place to go into too much detail, but let me offer a couple of definitions:
"The written and unwritten body of rules largely derived from custom and formal enactment which are recognised as binding among those persons who constitute a community or state, so that they will be imposed upon and enforced among those persons by appropriate sanctions." 
"The body of rules and guidelines within which society requires its judges to administer justice" - Lord Scarman
Activity: See what you can find in the way of definitions on the Internet.
What then is Public International Law?Edit
Public International Law discusses on matters as the law of international organizations, the law of treaties, human rights, humanitarian law, international courts,etc.(Zarefar, A. at fa:wikipedia)
- Curzon, L.B. 'Dictionary of Law' 5 Edn. (Financial Times, Pitman Publishing, 1998), p. 215
- Duport Steels v. Sirs  ICR 161