A strategy came is a genre of computer games, that involves controlling units and buildings, and maybe use casts, to destroy an enemy force's units and buildings. It is emphasizing strategical or tactical thinking and not necessarily a very effective way of moving one's character or units. There are on the other hand many strategy games, that can involve very elaborate means of moving units and using attack commands properly, the so-called micro management. But usually considerations such as an effective economy and proper build up (macro management) play an even greater role. A bad macro management usually cannot simply be compensated for by micro management. Also a bad choice of units against a certain composition of an attacking force can put a player at a great disadvantage, that micro management cannot compensate. On the other hand using casters wrong can put all efforts to waste, so micro management is not to be underestimated.
There are variations of strategy games, such as Real Time Strategy or Turn Based Strategy.
There is a very important difference between the meanings of the word strategy and the word tactic. Strategy aims more at a grand concept of defeating an opponent while tactics are more small-sized. A crude discrimination might be, that tactics describe more how you achieve something while strategy describes what is to be achieved.
For example the decision whether to go for a more economy-driven game instead of an early attack campaign can be considered strategy while the selection of proper units for the actual attacks and their deployment is tactics.
The distinction also depends on the kind of game you play, respectively what game mechanics are involved. While in Starcraft grand scale strategies are not really an issue (and on the other hand, very early skrimishs are very common), in games such as Supreme Commander or Company of Heroes it might very much make a big difference how you plan on progressing your campaign to take map points. Actually early attacks on a great Supreme Commander map might not even be feasible, as traversing the map simply takes too much time to use rush tactics or early reconnaissance.
This is why some people say, the term “strategy game” does not fit most of the games considered of that genre. They might more accurately be described as “tactic games”.