Home Brew Start Kit's are made of the equipment needed to brew your first batch. The equipment for brewing isn't at all that strange or unique, its just not exactly that common. For example, many of the start kits come with some type of carboy or food grade bucket for fermentation. Its important that you use very clean, and sterile buckets or carboys for this. If you have old buckets that you have used for anything other than food, or if they are scratched or have signs of wear and tear, it is much better to start with a new one.
The choice of going with a bucket vs a carboy is really up to the home brewer. Either will do just fine. The carboy gives you a some visual indicators of whats going on inside, without having to remove the lid. It also allows you to see the trub that has settled to the bottom during the fermentation process. In the end either choice will work fine as long as they are adequately sealed with an airlock.
The airlock for brewing beer is one of those necessary pieces, yet is not going to be commonly found around the household. It is designed to let air our of the fermentation vessel, and not let air in. As fermentation is underway, carbon dioxide is being released. This gas needs to escape in order to avoid pressure build up. The airlock is what allows this to happen.
Other than the items mentioned, the starter kits that require bottling, will come with a bottle capper and caps. The capper is a lever-based contraption that, without much effort, allows you to pop a cap right onto a bottle. It makes bottling a case or two of beer fairly simple....and the end product (a couple of full cases), is indeed the reward.
The best home brewing starter kits come in various shapes, forms and prices. Some of them would be considered investments, as you can use this equipment over and over. Some also come with the recipes ready to go for your first batch.