The Traditions are the Law of the Camarilla, initially predating the sect, some saying they come from the earliest Kindred. They have been re-ordered and reworded over the years, but the tenets hold true, and since the foundation of the Camarilla, provide the backbone and codification of the preservation of the Kindred.
The First Tradition
Doing so shall renounce thy claims of Blood.
The most important of the Traditions, the other five all tie back to the Masquerade. Kindred are taught to keep their very existence a secret from the mortals and other supernaturals around them. Being immortal, it is at times better to remain hidden and let your enemies die than confront them.
The Second Tradition
None may challenge thy word in thy Domain.
This establishes the authority of a Kindred over their domain. While some semantic purists try to extend this to a hunting ground or haven, it is accepted that the Prince has control over the domain of the city and the kindred in it.
The Third Tradition
If thou createst another without thine Elder's leave, both thou and thy progeny shalt be slain.
In order to preserve the Masquerade, population control is needed. The "Elder" in this case is generally considered to be the Prince of the Domain, but at times has been interpreted as the Kindred's sire or Primogen, it depends on the generosity of the Prince.
The Fourth Tradition
Until thy progeny shall be released, thou shalt command them in all things.
Their sins are thine to endure.
You are responsible for any new Kindred you create. Teaching them how to control their beast, feed without being seen, the rules of prestation and status, how to behave in court, and these very Traditions. You are responsible for the errors and crimes and can face the same punishment. When a Kindred is ready to be released into the Camarilla as their own person, they are present to the Prince of the Domain who Acknowledges them.
The Fifth Tradition
When thou comest to a foreign city, thou shalt present thyself to the one who ruleth there.
Without the word of acceptance, thou art Nothing.
When in someone else's domain, you respect them and it and behave appropriately. When you travel to a different domain, you must get permission from the Prince to be in that domain.
The Sixth Tradition
The right of Destruction belongeth only to thine Elder.
Only the Eldest among thee shall call the Blood Hunt.
Killing other Kindred leads to violence that may cause a breach of the Masquerade. You need permission from the Prince to kill another Kindred in his domain. The Blood Hunt is for the worst of crimes as it turns all Kindred against the one hunted. Only Princes can call that.