I am surprised that a more up-to-date answer is not added here yet. Endgame tables is one area where major improvements happened (see Nishanth's answer). But, I think the opening is the main area revolutionized by the AI wave. By the way, these are not the only areas of remarkable improvement. In fact, some engine games are now featured in the list of games that revolutionized chess (e.g. see the article 7 Games That Transformed Chess). According to the Authors of Game Changer, the book on AlphaZero, the engine gives more importance to piece mobility and king safety, compared to non-AI engines or even most humans. Studies on what factors these advanced engines give more importance to could revolutionize chess theory as a whole. After all, ascertaining the importance of chess themes in a way different from the traditional wisdom is exactly how many movements in chess theory such as hypermodern school were born.
Opening is one area where AI wave made remarkable improvements. AI-based engines have introduced several opening ideas that challenge conventional wisdom, and some that use the known ideas in novel ways.
Quote from a chess.com article:
Before the advent of engines, opening theory was largely developed
through human trial and error over decades of play. Grandmasters would
experiment with different lines and ideas, and over time, certain
lines would rise to prominence while others were discarded.
Today, engines have accelerated this process exponentially. Top
players use engines to test out new ideas, find improvements in
well-known lines, and discover new theoretical novelties that could
catch their opponents off guard.
Specific examples for this include those mentioned in the following quote from the article How Chess Engines Have Shaped Grandmaster Play?
Chess engines have revolutionized the study of openings, enabling
grandmasters to delve deeper into established lines and discover
entirely new variations. For instance, the Ruy Lopez, a classic
opening, has seen an explosion of new ideas thanks to engine analysis.
Grandmasters now use engines to refine and innovate openings, as well
as to uncover hidden resources. An example of this can be seen in the
World Chess Championship match between Magnus Carlsen and Fabiano
Caruana in 2018. In Game 1, Carlsen’s novelty with 6.d3, discovered
with engine assistance, caught Caruana off guard and set the tone for
the entire match.
A quote from another chess.com article.
AlphaZero's style was deeply counterintuitive for a human and a bit
closer to the Romantics or Tal than most chess players would probably
have expected. "AlphaZero appeared to target the opponent's king
directly from the opening moves and sacrificed material freely to
achieve its goals," wrote GM Matthew Sadler and WIM Natasha Regan in
their book on AlphaZero, Game Changer.
A specific example is featured in the article Stockfish On The Classics: Kasparov's Gambit.
For more specific examples and details of what we learned from AI engines, see videos in the Learn from the best series in chess.com. Some compilations from these series: Leela, Stockfish. The videos in the stockfish compilation specifically feature opening ideas.