As far as astrophysics is concerned, the main categorisation of a planet is through the Planetary Classification List. This breaks planetary bodies into groups, classes and types. See that page for a complete discussion.
Planets have other attributes as well though. Some of these are simple numeric values (such as radius, density etc).
The Habitability of a world defines how habitable it is for humans. It ranges from I (ideal garden world) to VI inhospitable hell hole.
Habitability I worlds are ideal places to live. There are large parts of the world where a human can live naked (or at least with very minimal clothing) indefinitely. There is also plenty of food available to allow someone to live off the land without external support.
These are ideal targets for colonisation, since all they require is a bit of starting equipment and knowledge of basic farming and survival skills.
Habitability II worlds are reasonable places to live. It's possible to survive naked on large portions of the surface for a long period of time, though temperatures may be too hot or too cold to make this a comfortable proposition.
Edible food may be scarce or non-existent, so even a new colony may require regular supplies from off-world either in terms of basic food, or equipment and chemicals for purification or soil fertilisation.
Habitability III worlds are difficult to live on, requiring some form of life support. This may be in the form of oxygen masks or extreme weather clothing. A full vacuum suit isn't needed, so unprepared visitors may be able to survive for a few days with only the minimal of equipment.
Some type III worlds are pleasant in all but atmosphere - so a lush garden world with a Carbon Dioxide atmosphere may have no clothing requirements, but require a full oxygen mask.
Habitability IV worlds require a full vacuum suit for survival on the surface. Any colonies will need to be completely sealed, with their own internal life support. Plants and animals do not grow on the surface. Class IV are commonly vacuum worlds which are neither too hot nor too cold.
Habitability V worlds suffer from a range of issues that make them hostile to human life. They may require excessive cooling or heating, lack any form of breathable atmosphere, or generally suffer from an actively poisonous environment which needs special shielding against.
Class V worlds are avoided by settlers unless there is a really good reason.
Examples of class V worlds would be Mercury (too hot) or Pluto (too cold).
Habitability VI worlds generally suffer all of the problems of type V worlds rolled into one simple package, requiring very special survival gear to last more than a few seconds. They may have excessive atmospheric pressure, high temperature and acid for rain for example.
Examples of class VI worlds would be Venus or Jupiter (the surface of which is inhospitable). Note that in both these cases, though their surfaces are considered habitability class VI, their upper clouds are far more hospitable and some colonies may take advantage of that fact. The upper clouds of Venus could be considered III.
Though some survival suits are rated for type VI, such worlds vary so much in their hostility they often require a uniquely tailored solution for surviving on the surface.