What type of camera or software, do I need to achieve that?
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You need a camera with a relatively large sensor and a fast lens. What you are seeing is actually a property of optics called Depth of Field. Only a certain distance from the camera can be in focus at any given point for a given aperture and focal length. The degree of how out of focus it appears is also relative to the size of the image being projected (thus the distance from the point where the image inverts) and thus, larger sensors show more blur.
Cheap cameras often use very small sensors and thus have a hard time getting a shallow depth of field, however any DSLR will achieve it quite easily, as will any more professional video camera with a larger sensor. Shoot with the aperture as wide open as possible and try to have the camera relatively close to the subject with the background as far away as possible.
Technically, increasing focal length will also decrease the depth of field, but then you have to move back from the subject which will increase it again. You want a small depth of field close to the camera so that the background can be significantly out of focus. If it is too out of focus, you can adjust the aperture or the ratio between the camera, the subject and the background to make it less blurry (by expanding the depth of field).
You can also use many online Depth of Field calculators to figure out a shooting situation with a particular camera prior to trying it in real life. They won't visualize it for you, but they will give you an idea of what distances will be in focus and which will be out. There are also lots of great articles on depth of field over on our Photography sister site, though they don't deal with video specifically, but the principal is the same.
In a pinch, you can fake it as well using masks and blurs, but that's really not an ideal way to do it. In camera always looks better.
The simplest way i suggest is to blur the background with video editor after shot by your recorder. It's not hard to operate, check this tutorial about How to blur Something out in a picture or video with Adobe photoshop.