You can help keep other people's hyperdrives online by contributing bandwidth. This is called "hosting."
To host a drive, visit the drive and click on the peer count on the right side of the address bar. You will see a toggle. Switch it to the green "on" state.
You can turn off hosting by toggling the button again.
To see the drives you're currently hosting, open a new tab and click on the ellipsis icon underneath your pinned bookmarks. Then click on the "Hosting" link.
You can stop hosting drives in that listing by right-clicking on them and selecting "Stop hosting."