In the Witcher III there are some things different. First, the previous two Witchers were more closed-world. In Witcher III, the world is open. This can be kind of confusing for casual gamers who are just pure fans of the series, but let me make a very apt comparison. Witcher 1 & 2 are similar to most action RPGs (like Fable) in the sense that you are in sort of a open area, but it's limited in size and you move section to section, while the Witcher III is very much like "The Elder Scrolls: Skyrim."  

Witcher III has a vast open world and it's very different than the previous games. The first major thing to note is fast travel. Fast travel didn't exist in previous games, the maps were small enough that you could quickly walk back to the quest area. In Witcher III you fast travel by opening your map, selecting a landmark, and then choosing to travel there. 

Now, on to the open world. The key difference here is that side quests are completable at any given time in the main story (once they've unlocked in the world and you've found them). As such, you'll explore areas away from the main quest series to complete them. Contracts also return, one of the early contract quests is to deal with a noonwraith. You'll travel to a well in the middle of nowhere and then descend into it, with a list of tasks to complete. 

The open world also comes with a variety of "living world" elements. Throughout the world will wander various strangers walking the roads. Aggression towards them can lure the ire of guards. 

Another option to travel in the wide open world is your horse. You can double tap left stick or use the PC key assigned to summon. Roach, the name Geralt gives to all of his horses, will be your trusty companion throughout the game and assist you from moving from a waypoint to your objective which is listed on the map. 

Exploring is also a big feature. While riding around on your house the living world can draw you in. You might see an oddity on the side of the road or something to explore and when you ride over to it you'll see a new sidequest for you to complete. Witcher III doesn't have invisible barriers, so you can explore most everything, including Geralts ability to jump over obstacles. 

Travel Methods:

By Ground 

You have a few options to travel ground. Well, one option to travel by ground. You can press shift to sprint. 

By Horse 

You can travel by horse by pressing "X" to call your horse. While on horse you have the following options available: 

You can follow the road on auto-pilot by holding down shift. 

You can gallop quickly by double tapping the shift key. 

Your horse by and far is going to be your main route of travel. 

Horse Combat 

You can fight while on the horse. You can swing your sword as usual, but there is a horse fear bar at the bottom. When it's at maximum, you will dismount and Roach will flee. 

Certain quests will have you fight on horseback, such as chasing someone. A non-lethal way to deal with these is to cut someone down off of their horse (just aim to strike at the horse). It can be rather confusing at first, but after a few goes you'll get the hang of it. 

Horse combat is great against fast moving enemies, but it is clunky against beasts like wolves. It's often better to dismount and fight proper, but it's also a great way to take a larger group by surprise. 

Fast Travel 

You can travel the world in seconds with fast travel, but only to fast travel signposts. These sign posts are littered around the land near cities and encampments. Approach one and press E, which will then bring up the map and allow you to fast travel between other sign posts. 

There is no cost for this. 

You can also travel by boats in later maps. Boats only go to boats, signposts only go to signposts.

Locating Quests 

There is good reason to wander the land, especially on lower difficulty levels where it's easier to not randomly die in the woods. First, quests are different than contracts in that they give you objectives vs. giving you something to kill. Second, they are only available if you find them. You must explore the land at large in order to locate the various quests.                                                                                             

So to recap, Witcher III isn't linear, it's open. You can fast travel by opening the map and you can summon your horse, Roach, to help move around faster. Additionally, Geralt can sprint. There is the main story quest that takes you through the entire game, but tons and tons of side quests that you can complete at any time (the story quest will wait).  

Everything in the above paragraph is new to Witcher III and very much different than the previous games. Hope that helps your travels!