The Degrees of Freedom of an object represent its ability to move around in a space. In a three-dimensional space, there are a total of six degrees of freedom. Half of which represent rotational movement (yaw, pitch and roll) and the other half represent translational movement (moving along the x, y and z axis). In virtual reality, three degrees of freedom usually means the three rotational movements. A good example of this is the Google Cardboard, while it permits the viewer to look in every direction around them in the rendered scene, there is currently no capability to move about the scene by moving in real life. Any translational movement has to be initiated by some other input like tilting your head. While only having three degrees of freedom in limiting, it does have its uses, like 360 or VR video viewing on web browsers.
When people think of virtual reality, they usually think of it with six degrees of freedom. Allowing the user to not only look around, but also move around the virtual world and look from above or below objects. To have a true VR experience, the hardware must provide all 6DOF and provide both orientation tracking (rotational) and positional tracking (translation). Examples of these types of headsets include the HTC Vive and Oculus Rift.