I'm not related to the project, but I think they mean that it stores the audio locally, and can transcribe locally. They (plan to) use GPT for summarization. They said you should be able to access the recording locally too.

The rest of the company has info on their other free/paid offerings and the split is pretty closely "what do we need to pay for an API to do vs do locally".

Again, I'm not associated with them, but that was my expectation after looking at it.