Two terms, which seem to totally contradict each other, yet totally intertwined with each other. Now, when I say makes you better at strategy, I don't mean you being able to execute a nice plan without the fear of dropping a random piece exactly! The knowledge base of tactical patterns themselves have actually seemed to alter the way I plan in a game!
Ever get into a position where you had many pieces near the opponent's king, but wondered "But do I have anything concrete?" And that question pretty much distinguishes sound attack, from unsound! When you don't see those bishop sacrifices coming to open the king, when you don't see those sudden rook lifts leaping into the position within two moves in the blink of an eye, when you miss the tricky knight mate looming, it affects your sense of danger. If one could only judge an attack by how many normal moves it would take to get a threat underway, while missing possible sacrifices, things may look much less dangerous than they actually are; it totally changes how you evaluate that position! That's what tactical puzzles are all about though: you look for just the right move to break through, and seeing those kinds of ideas in games, even if they are just potential, can quite literally make the difference between a good and terrible plan.
But in a broader sense, it has made me think more concretely in general. In any position I no longer list certain features like isolated pawn, bad bishop, etc, as a means of seriously evaluating the position. I may mention them to myself, but I am not using those words to make any conclusion about the position at all. What's more important is if my position is achieving something, or if it can be expected to achieve something at some point. And the best way to achieve anything in a game is by tactics. If you have lots of fast, forcing ways to put pressure on the position and give the opponent problems, then you have control, and a good position; that's all you really need to know.
Let's look at an excerpt from a game of mine against an International Master:
The sheer fact that ...Nb4 forked c2 and d3 was the one thing that changed the evaluation of that position from equal to lost -- isn't that crazy? I lost a game for missing that minuscule thing!
Actually, if you take the position after 17 Nd2, then gently slide the pawn to a3, then it probably is pretty balanced! I think this proves that you have to be very wary of the specifics of a position, because in this case for example that a-pawn's position, on the always supreme edge of the board, has my fate in his hands.
Moreover, when looking at how many moves it actually took to put pressure on d5, that's what really gave you the idea whether they were weak or not, not the fact that they were classified as "hanging pawns."
Next time you see someone attack you, actually look at the concrete threats he will be able to come up with in the next 5 moves, and how easy it will actually be to prevent them before panicking at his aggressive gesture!
What do you think, do tactics make you better at strategy?