A Mana pool is a mage's reserve of mana. A mage can improve upon his/her mana pool to a certain peak, but the Mana pool is what limits a mage. If you go over the limit, you get Mana Burn, which kills many careless mages.
The size of a mana pool is what you're born with, and how much you increase it. Your mana pool will increase or decrease considering on how many spells you cast. Some people can't even use their mana pool because of a condition known as "Magical Ignorance". Dependent on the size of your mana well, you can be an ubermage, or a smalltime hedge witch. You have to play wth the cards you're dealt with.
A mana burst is when a mage attempts to absorb more mana than he/she is capable. If a Mage does absorb too much mana, their mana Pool will literally burst and they will, in most situations, die. Those who survive become Mana Masses.