Classically positional play is what is described in part 2 of Nimzowitsch's "My System". Part 1, The Elements, is more tactical in nature. It describes play in open files, using the 7th and 8th ranks, passed pawns, pins, discovered checks and a few other features.
Part 2, Position Play, deals with stuff like
Fighting for the center, which you do by moving pawns and pieces (firstly knights and bishops, later rooks) so that they occupy, support or attack the center.
Over protection of important points or squares, in the first instance central ones later they may be points important for attack or defence, is important because it strengthens those points. This in turn gives more freedom and flexibility to the pieces involved. They are not firmly tied down because other pieces are sharing the burden. And it gives prophylaxis. Because these points are over protected you are not going to get caught by a sudden attack from your opponent.
Certain static features are described and discussed which have positional characteristics. Doubled and isolated pawns are usually positional weaknesses. Very occasionally they may have good features but mostly they are bad. The IQP (isolated queen's pawn) is covered in great depth. Depending on how the two sides play the IQP can be a dynamic attacking tool or it can be a static weakness which will eventually fall.
The two bishops (when you have two bishops and your opponent has either two knights or one bishop and one knight) is positional plus because of the way they can work together. They can cut an impassable diagonal line across the board in the same way that a rook can cut such lines orthogonally.
Why are these concepts important? Well, when you first start playing you don't really know what to do with your pieces. As Nimzowitsch says you probably think you should get your pieces out, castle on the opposite to your opponent and then each of you should launch a pawn storm attack against your opponent's castled king. First one to break through wins. It can certainly be a lot of fun but it's just not going to work against somebody who has mastered a more positional way of playing.
These positional concepts give you guidelines of how to play when the position doesn't call for a tactical solution. In some respects it gives you guidance of how to build up your position so that you can either start your own tactical attack or frustrate your opponent's tactical attack.
Mastering tactical and positional play will likely take you to somewhere round about the 2000 level, which is no mean feat. To make progress much beyond this level you will have to start to learn and understand when to break these positional guidelines.
My System has many examples and games which Nimzowitsch uses to illustrate his points. He also wrote a follow on book of more examples and games called Chess Praxis which is highly recommended for further study of positional play.