I present two plans I gleaned from Silman’s Amateur’s Mind, one from the chapter on hanging pawns, the other from the chapter on initiative. The two go nicely together, though, because they are in fact both about initiative, in particular how to maintain as much of your own initiative as possible by taking control of what I like to call “intrusion” squares. Intrusion squares grant your opponent access to your position and create nasty opportunities for counterplay (or, if the opponent has the initiative, denying you counterplay by forcing you to defend).
By reinforcing intrusion squares, you deny your opponent this counterplay, which in turn reinforces your own initiative. As Silman likes to point out, the best defence is most often the potential for a counter-attack; the best offence, accordingly, is the offence that at the same time denies your opponent any form of counterplay.
In the example with the hanging pawns, you see how Qa5 reinforces the d5 square and in so doing keep an advance of the hanging pawns alive. Black’s plan is to make sure that the hanging pawns maintain some kind of dynamic potential and to prevent them from becoming a mere weakness.
In the second example, White has the initiative and a potential kingside attack. The move Qe3 does not develop another piece, nor does it further the attack, but it defends the d4 square and prevents Black’s queen from intruding on d4, thus stalling potential counterplay on the open d-file or avoiding exchanges that would dampen White’s initiative. Silman posits that in open positions, as a rule of thumb, the party who occupies the open centre file first gains the initiative; so Qe3 could be seen as an application of that principle as well.