What does it mean?

If your opponent is playing xxxx, he is ceding both the center and a spatial advantage.  Ever seen something like that?  So what? 

How should a center advantage or a spatial advantage be used?  Often an opening line will end with comments like "...Black has an advantage due to his control of the d file and a Q-side pawn majority".  Do you know what to do with it or even what it means?   This is the question you must answer, not what is Black's best move at ply 23 in the Najdorf Posion Pawn.

Difficult questions.

The advantage of a queenside mayority is that you can make a freepawn without exposing your king.

When you have control over the centre your piece will be more active than your opponents. There is not one way to play with it: sometime you attack the kingside, in other positions the queenside. Maybe there is some tactics to gain material.

With space advantage you have more space for your pieces. Most time its easier to switch from queenside to kingside and opposit. Yoy have more room to play your pieces to better squares.

I think you must buy a book about making plans in chess and about pawn structures. With examples you will find an answer to your question.

Good luck with the search

Actually I have some of the answers, execution is sometimes faulty, but rather my post is for those who ask "deep" questions about the openings, or chase down variations and end up with the ubiquitous +/- and still lose a game because they don't know.

Good books include Pawn Structure Chess, Positional Chess, Judgement and Planning in Chess, among many others.

well I think that it's best to just keep improving your position and hindering your opponent's (unless their king is extremely weak then a rushed attack may be best). Then when you get a clear advantage, come up with a plan, usually attacking a side of the board and if you have the better game it's more likely to be succesful and if your opponent has a worse game then it's harder for them to execute their plan.

And how do you improve your position?   The steps necessary to improve a position vary depending on your advantages, disadvantages and imbalances.  The proper plan to improve your position when you have a pawn majority is different than when you have greater space, or mobility, or center control, or initiative or weak King, or bad bishop, or weak squares, etc.  (For that matter, how do you gain one of those advantages?) If you move pieces until you have a clear advantage you won't get one unless your opponent cooperates. Wish Chess is bad strategy. 

To say "improve your position" is the same thing as saying "play good moves".   In otherwords, nothing.  That is my point and that is where many of the conversations in this forum end.  Those who are claiming superiority for an opening or variation, those who are propounding on a system or attempting a new line should ask these questions and maybe answer a couple of them.

The French defense, esp the Winawer variation, features locking pawn chains which preclude most action in the center. This means White will attack on the Kingside and black on the Queenside and so forth.... Talk about the Bishop pair, Black's often (very) bad bishop, the open g & h files black attacks on (Winawer Poison Pawn var).  20 moves of analysis pales in comparison to getting Black to attack the pawn chain and white to take away the outposts from Black's knights.

If you say your opening has an advantage you should be able to say what that advantage is, and how it is to be best utilized.  I don't want to see variations I want, I can make b5 a strong outpost for my Knight and put pressure on his weak d6 pawn via the Knight and the half open d file.  My opponent has a slight initiative and possible attack on my King side which will have to be neutralized by dening him posts for his pieces, avoid creating holes in my kingside and possibly trading off his attacking pieces.

Do you see what I am talking about?