TileDB is designed primarily for persistent storage, similar to HDF5, Zarr and Parquet. TileDB is a cloud-optimized, dense and sparse multi-dimensional array storage engine, which is broader than Arrow's Dataframe. In addition TileDB also handles updates, time traveling and partitioning at the library level, which are not possible with the Arrow project's current choice of persistent format, Parquet. TileDB removes the need for using extra services like Delta Lake for updates or Hive for cataloging and partitioning, as you get all this functionality in a single, embeddable library.
https://people.csail.mit.edu/stavrosp/papers/vldb2017/VLDB17...
The basic jist is: TileDB is substantially faster than alternatives for random writes/reads - this allows for more sophisticated parallel linear algebra algorithms as well as evaluation of predicates.