Steinitz himself was a strikingly brilliant player, but at some point he was converted from an enthusiastic disciple of the attack and became obsessed with the evils of the carelessness, flashiness and frequent unsoundness of that that method of play.
Morphy's natural development, logical preparation and accurate execution struck a chord and Steinitz developed an interest in defense to the point that it became his passion; he was fascinated by the idea of refuting an unsound attack, of demonstrating to the opponent that one cannot lightly toss away Pawns, not to mention pieces, without being punished. Hit-or-miss, helter-skelter attacks wouldn't do.
While Steinitz appreciated the play of his greatest rivals, Zukertort, Chigorin and Blackburne, their attacking play was purified and raised to finer artistic levels by his criticism. His theories had a lasting effect on the chess world whether the great masters agreed with him or not, they absorbed the fundamentals of his theories into their own styles.
According to Steinitz, at the beginning everything is in equilibrium and correct play on both sides maintains the equilibrium and leads to a drawn game. Therefore, wins come only as the result of an error. There is no such thing as a winning move, only losing ones. As long as the equilibrium is maintained, an attack cannot succeed against correct defense. Winning positions could not be obtained by inspired attacks and unsound sacrifices. Therefore, you should not attack until you have an advantage, caused by the opponent's error, that justifies the attack.
His beliefs also had an effect on openings. A player should not at once seek to attack, but instead should try to disturb the equilibrium in his favor by inducing the opponent to err. Steinitz believed that all gambits can be defended.
When it came to defense, Steinitz taught that one must be prepared to defend and make concessions if necessary, but don't make them until forced to do so and then only make the required to meet the threat.
There's an interesting debate about the advice on attacking: once a sufficient advantage has been obtained one must attack or the advantage will disappear. Who said that? Steinitz or Lasker? The answer depends on what historian you read.
Speaking of Steinitz, Henry Bird wrote that if you put the pieces in a hat, shook them up and dumped them on the board you would get the style of Steinitz. Bird was joking, but for players who were used to the straightforward attacking styles of Anderssen and Morphy, Steinitz' sometimes time wasting and weird looking moves to obtain some seemingly trivial advantage just didn't look right. But, it was from those moves that players learned about strategy.
In the following game Steinitz delayed castling, made some odd looking moves and his N took a journey starting at move 19 and when it reaches c6 at move 27, he had a won game and black resigned shortly thereafter. It's interesting to note that here were no tactics in this game. Steinitz just squeezed the life out of his opponent.