The game is drawn because with the remaining material no sequence of legal moves can lead to a checkmate.
Syzygy tablebases allow perfect play with up to 7 pieces, both with and without the fifty-move drawing rule, i.e. they allow winning all won positions and bringing all drawn positions over the fifty-move line.
The tables provide WDL and DTZ information. Forcing captures or pawn moves while keeping a win in hand ensures that progress is beeing made.
DTZ optimal play is unlike the shortest way to mate, because DTM does not account for the fifty-move drawing rule: Sometimes it is better to reset the fifty-move counter than to go for the shortest mate.
If you want to use tablebases in a chess engine you certainly need a local copy.
Most of the time (during search) only WDL tables are used. Keep these on SSD storage if you can. DTZ tables are generally only used to finish the final phase of the game ("at the root").
|3-5||378.1 MiB||560.9 MiB||939.0 MiB|
|6||67.8 GiB||81.4 GiB||149.2 GiB|
|7||8.5 TiB||8.3 TiB||16.7 TiB|