>Okay, so for a use case like The Pirate Bay, which is a popular database of magnet links and related metadata (Description, who added to the database, when added, etc). Users search this data in various ways.
The problem with this search index is that it requires all of the .torrent files containing the metadata. In lbry this metadata (as well as more rich fields) are stored to the blockchain, so any full blockchain node has the information to provide more sophisticated searches. Chainquery is what runs a full node and provides the search engine for the UI (https://github.com/lbryio/chainquery).
>As in, how would a user search it or find popular torrents?
As indicated above, if they're using the UI it provides a search engine via chainquery. Torrents are also not a currently supported source type for a download, however there is nothing to stop it from being added.