How would one go about caching / managing many large files (videos) on a user's computer via browser mechanisms (plugins are acceptable solutions). From what I can tell, local storage is about database type data, not files.
The FileSystem API[1,2] was going to be your best bet going forward, at one point it was very much bleeding edge. However it has been been abandoned by w3c. From their own documentation:
Work on this document has been discontinued and it should not be referenced or used as a basis for implementation.