I assume it will be a precursor to Hydra, but I haven't heard it talked about very much.
You can learn more about the Basho phase at the Cardano Roadmap, but I will briefly summarize what it says.
The Basho phase is focused on improvements to scalability and interoperability, this will improve the performance of the Cardano network as it grows and transaction volumes increase. One important core development this phase will bring is the implementation of sidechains, which are new blockchains that are interoperable with the main chain. Basho will also allow for parallel accounting styles, meaning that while the main chain uses the UTXO model, a sidechain could use account-based models giving the ability to support and switch between the two models.
I hope my brief summary helps, but you should definitely look at the road map for more information.
Scalability! In simple terms, it brings "continuously improving" scalability! That means by design we will be more and more scalable as we grow. The exact opposite of Bitcoin. Currently Cardano has around 1000 TPS. What Hydra brings to table is making each SPO a node of Hydra. That means each SPO would be capable of 1000 TPS. That means the more Stake pools, the more throughput for Cardano after Hydra. With an example of say 1000 stake pools (very conservative since we already have 2000 plus), Cardano's throughput would be 1 Million TPS (1000 * 1000).