The Knightfall story-line in 1993 began the change from the unarmored (or lightly armored) Batsuit to more rigorously armored suits. Batman, in his confrontation with Bane, has his back broken and is nearly killed. You can see from the picture below, Batman is still wearing the version of the suit made popular by Neal Adams.
While Batman is incapacitated he is replaced by the reformed assassin Azrael, John-Paul Valley, who uses a mechanized suit to augment his physical abilities.
After his defeat, Bruce Wayne enlists the aid of Dr. Shondra Kinsolving to rehabilitate him and asks Jean-Paul Valley (Azrael) to take up the mantle of Batman so that Gotham has a protector.
Valley tailors his costume and redesigns it becoming the protector of Gotham as a highly armored, technologically advanced version of Batman. This armor, and how Valley used it inspires a new kind of terror in Gotham. Valley cares little for collateral damage and is indiscriminate in his use of his abilities.
Valley finds and confronts Bane and with his powered armor, is able to hand Bane a crushing defeat. He all but considers killing him but sends him to Blackgate Prison as Batman would have done. However, choosing Valley as the new Batman came with a high cost. Bruce would lose Alfred, alienate Nightwing (Dick Grayson) and risk his good name in Gotham, due to the near homicidal behavior of Valley.
When Batman is rehabilitated in the conclusion of the Knightfall, Knightquest and the Knights End saga, he introduces a new suit in Troika, made with stronger materials, armor plates and a new Batmobile.
This suit strongly resembled the Batman armor from the movie Batman (1989) with Michael Keaton.
There is a related article here on the Stack regarding the Bat-armor: Why doesn't Batman make an armored suit like Ironman?
If you are curious to see more of how Batman's costume/armor has evolved you can look at the Batsuit entry on the Batman Wiki.