There are two important reasons why your new kitten should be quarantined for a minmum of two weeks. First, the stress of being ripped from all familiar surroundings and people, traveling to a new home, and meeting a new family is very stressful on a kitten. This can sometimes cause health problems by suppressing the immune system, just as it can in humans. Cats in general are very susceptible to certain illnesses and a stress response can trigger an illness such as an upper respiratory infection (cold) or a bout of diarrhea. If there are other cats in the household, it is always a good idea to keep them separated until you are assured that the new kitten is not going to succumb to such an event.
The second reason is that the kitten needs to be kept in a small room where it can easily find its food, water, and litter box. It also needs this time to get to know it’s new human family and to develop a bond with them. A new kitten being left to wander freely in a new home when first arriving can easily be overwhelmed and at the least have some litterbox mishaps because it forgets where the box is, or at the worst hide in as safe, dark environment (e.g., under a bed), which will necessitate you ‘chasing after’ it to retrieve it. This can cause even more fear and stress in the kitten and set up an unhealthy relationship between it and you.
When a kitten is restricted to a single room such as a bedroom or a bathroom with only you going in and out to interact with it, it will soon learn that you are the center of it’s life and a strong bond will form. Once this has been accomplished, you can start to slowly introduce it to other parts of the house, and to other pet members of the household as well.