Ken's Comments ...
Re: Classed as moving your Pieces (and Pawns?) from their starting positions to squares that attack either the Center or the Kingside squares (or, should that be squares close to the Castled King, whichever side of the board he's on?)
The Center and the side (quadrant) where you have an advantage. Many times one side will have an advantage on the Kingside, while the other will have an advantage on the Queenside. Your play should be conducted where you have the advantage, in general, unless you are under attack. If that side where you have the advantage happens to be the Kingside, all the better.
Re: If your material claims better square (as just defined in the last bullet point) then your opponent, then you have the advantage of Superior Development (and one plus point).
A little too simplified (even though I like to keep things simple).
Generally, a good rule of thumb is to move one or two pawns in the opening, as well as just one move per piece until your rooks are connected (see p. 176, 1st 3 paragraphs). You want to have more pieces developed than your opponent, not pawns. Imagine the first 8 moves for White if he moved each pawn to the 4th rank one by one. You would probably be checkmated before another 8 moves could happen. You move one or two pawns to allow your pieces access to the board, because pawns support pieces, and pieces shouldn't have to support pawns. In modern chess openings, sometimes these "thumbs" are broken, but until you have grasped the essentials, don't break your thumbs!
For now, the easiest way to determine superior development is count the number of pieces that are actively in play verses your opponent. If you have more pieces in play, you have Superior Development. On p. 181, paragraph 1, H&M-S recommend counting "the number of pieces of each color off the back row, plus any developing moves on the first rank itself (castling; a rook move to a central file)".
Also, it would consist of pieces in the subcenter (Knights especially not on the a-b and g-h files unless for a very good reason - they have less squares they can go to), or influence the center (Bishops, Rooks, Queen can be on the a-b or g-h files, but they need to exert pressure toward the center or to the scene of the action). It also consists of tempo (see p. 179, bottom paragraph).