Four Days is the minimum amount of time you would want to spend visiting Disney World. That gives you exactly 1 day to visit all the zip code sized Disney World Theme Parks: Magic Kingdom, Hollywood Studios, Epcot, and Animal Kingdom. With all the shows, eating venues, rides, and parades each park has you'll want to stick around for the whole day to experience it all.
Remember, Base tickets let you visit one park per day. For instance, you can go to Magic Kingdom on Monday then Epcot on Tuesday. One park per day. You can leave the park and return to the SAME park, later in the day, if you wish. You cannot leave and go to another park.
Hoppers will let you visit MORE than just one park per day. For example, you can visit the Animal Kingdom in morning (the animals are most active at that time) then go to Epcot at night to dine at the Bistro de Paris. You can hop between the parks as many times as a whole day will allow. Water Parks are NOT included.
Plus tickets let you visit the Disney Water parks in addition to the big theme parks. So, you can go to Hollywood Studios to start off the day then, when it gets hot, you can go cool off at Blizzard Beach. You will use up 1 theme park day and 1 water park visit by doing that. You can also just spend the whole day at a water park if you so desire. Hopping between the big theme parks is not permitted with these tickets.
Premium tickets let you Hop between the theme parks AND visit the water parks. These tickets give you all the options Disney has to offer. Visit Epcot in the morning, splash around at Typhoon Lagoon at midday, then catch the fireworks at Magic Kingdom at night. You have the option to really cover a lot of Disney ground in a day with Premium tickets.