Package bees are bees that are shaken out of colonies into a screened box, given a queen and a container of food sufficient for transit. They are produced early in the season in warm climates and can build up quickly, so in about 10 weeks they are ready for the nectar flow. They are packaged by weight, which varies between 2-5lb, with apparently 3lb being the most common.
Packages are a major part of beekeeping in warm countries, but are rarely used in cooler climates. For several years after the hard 1962/63 winter in the U.K. many packages were imported from the U.S., but they weren't very successful. Many were headed by Italian or Starline queens that were very prolific. Nosema was a big problem and many colonies were lost. I bought 42 colonies from another beekeeper who was giving up and 19 of these were American packages the previous year. I lost them with nosema the following winter.
I have been unable to find out much about the history of package bees, but my guess is they were developed in the Southern States of U.S. and shipped north to start new colonies in the spring. Perhaps many went to Canada where they used to kill the bees, before they developed the wintering techniques they use now. This is conjecture and I would appreciate information please.
One major reason for their success is the 10 weeks needed between hiving and nectar flow. In countries like the U.S., packages can be produced early in the southern states and shipped to the northern states for the later flows. They do not seem to work well in cooler countries such as the U.K. They are effectively a swarm which would be an easier or cheaper way for a beginner to start.
Package bees have may uses including starting new colonies for commercial beekeepers, making up for winter losses and bolstering weak colonies. It is the most common way of starting for American hobbyists.
I have no idea when packages were first developed, but the Baton Rouge Bee Laboratory lists amongst its research achievements of 1920s - 1930s "Problems in producing and shipping package bees and queens", so presumably some time before then.