Package is bigger, usually something like a box that gets delivered. Pack is usually a few things bundled together. For example, in a store, two bottles of shampoo wrapped in plastic (buy one get one free) would be called a "2-pack". Packet is similar to "pack" but smaller. We often use packet for papers bundled together and placed in a folder, envelope, or wrapped with a rubber band (ex: welcome packet, instruction packet, application packet.)

With reference to my answer and to Allyson's. I'm English, and Allyson appears to be from the US. You need to be aware that US and UK usages are not always exactly the same.

Tricky one. I'd say this. A package will be something that's been wrapped up, and very likely something that's then sent somewhere, for example in the post. The word refers to the whole thing - the thing that's sent - not to the thing inside it. Pack can be short for "back-pack" meaning a rucksack. We also speak of a "pack of cards", but that's perhaps a slightly different meaning. The letters "et" suggest something smaller. So packet suggests a smaller pack. But "packet" is in fact in rather the more common use than "pack". Typically a packet would be a cardboard box with perhaps some food item in it which you would buy in a shop - eg a packet of cornflakes, a packet of tea. If you wanted to, you could say a pack of cornflakes, but packet would be more common I think.