I'll answer the original questions of this post before making any other comments.
How much can he move around when hidden?
The shadows conceal him while he moves (and for as long as he remains within 10' of some shadow). So, he would just have to make a Hide check as part of his move action, including any applicable bonuses or penalties.
Is it meant to be an "invisibility"?
In my campaigns it is a limited form of invisibility. As a supernatural ability for Shadowdancers, it is basically invisibility that is limited to immersion in or close proximity (10') to existing shadows (other than his/her own). If they leave the shadows or the shadows are removed, then they are as visible as anyone else.
What does a shadow mean? Is it any shadow not cast be himself of any size?
Again, this is my interpretation used in my campaigns. The shadows that can be used are any shadows of any size cast by anyone or anything other than the Shadowdancer.
I just finished a Ravenloft campaign with a Shadowdancer PC. Whenever he used his HiPS ability, I always described it as the shadows moving as if possessed of their own life and swallowing him from the sight of others. This made it a lot more interesting and eerie for NPCs as well as the PCs (including the Shadowdancer) rather than simply stating that he disappears.
I enjoyed reading the different takes on the ability in this thread. However, my attention was grabbed by the back and forth between Thanee and UltimaGabe. There shouldn't have been any arguement. Thanee nailed it on the first post.
True Seeing reveals the shadowdancer, since the HiPS ability is supernatural and therefore magical in nature.
That's all there is to say about it. It's a magical ability for Shadowdancers, True Seeing penetrates magical effects that conceal or disguise. The ability of the spell to penetrate normal and magical darkness eliminates any possibility of concealment in shadows (the presence of which is required for HiPS to work) from the subject of True Sight who can see in darkness.
UltimaGabe's arguements about True Sight's limitations vs. HiPS are based on flaws. The requirement for shadows for the ability to work is not "flavor crap". By requiring the presence of shadows it is implied that (in whatever manner the DM decides) shadows are used to conceal the Shadowdancer--otherwise, no such requirement would be in place. Now since darkness is darker than shadow and True Seeing (TS) allows sight in darkness, the person with TS would clearly see the person using HiPS. TS does not foil physical means of concealment (fog, physical disguise, etc.) but darkness and shadow are not physical obstructions, they are ambient conditions of visibility which TS allows the subject to see clearly in.
What UltimaGabe is missing is the purpose of the TS spell; to see through all forms of magical concealment. Could the spell description have been worded better? Yes. Without a doubt. Did the writer/editor list every possible method of magical concealment? No. They don't have time or the space for that amount of text. They rightly believe that the DM, and not some rules-lawyer PC, will deduce the purpose and effect of the spell and what it can and cannot do. The PHB would be three or four times its already considerable size if spell descriptions had to include every possible situation that the spell can and cannot be used for. That has nothing to do with the spell being open ended or not. It gets the point across; TS penetrates magical concealment, not physical. The supernatural (magical) ability to use any shadow of any size within 10' to Hide (conceal) yourself from sight easily falls within the purview of a spell designed to penetrate magical concealments.
UltimaGabe is also assuming that he is the authority on flavor text and rules text and he is basing much of his arguments on that which is faulty logic. And he is wrong to say Thanee or anyone else is wrong about their decision on the matter. TS allows the user to see in darkness. If you can see in darkness you can see in the shadows that a Shadowdancer is magically manipulating to conceal themselves.
As for the Ranger ability of the same name, it only works in natural terrain which kind of makes sense for a Ranger. There are too many movies to name as an example where someone is hiding in plain sight (Predator after the waterfall with Schwarzenegger in the mud comes to mind) in natural terrain. That doesn't seem too far fetched or outrageous for a Ranger of that level.