Which RAID level mirrors one hard drive with a second drive so that the same data is written to both drives?

That is RAID 1. It uses two drives with identical data so if one fails, you have the other drive.

One variation of RAID 1 used by certain controllers is to write as RAID 1 but read more like RAID 0 (but without the striping). That way, you have the write protection of a mirrored set, but can use the two drives to do interleaved reads for a read performance boost.