Here is sample metadata from one of the tweets sold: https://explorer-mainnet.maticvigil.com/tokens/0x28009881f0F...

This data is stored on the Matic blockchain. The most important bits are

1) Text contents of the tweet

2) Canonical link to tweet (on twitter)

3) Digital signature by owner (using their ethereum wallet)

Valuables (the service minting tweets) is also responsible for linking a twitter account to an ethereum address. Also, these tweets are purely collectibles, i.e. they don't confer copyright or commercial rights to the buyer.