What's the point of having a RAID 1 configuration over incremental backups to a secondary drive?

I have a synology NAS and I don't understand the point of RAID 1 system. Why bother having a mirror? If I delete a file by accident it's deleted on both drives.

RAID is not a backup mechanism; it's a redundancy mechanism, and it does a completely different job – one protects against disk failures, the other protects individual files. So you wouldn't use one instead of the other; you'd normally use RAID along with backups or snapshots.

The main advantage of a redundant system is that it will not go down completely when a complete disk failure happens – the mirror allows you to continue using the NAS without interruption while the array is rebuilding.

(In other words: If you had a backup system but no RAID, you'd have to spend time restoring the complete system from backups every time a disk failed. If you have a backup system and a RAID 1 mirror, you only have to use backups when both disks fail at once, which happens much less often.)

Likewise, the redundant array should also allow you to replace disks that are only about to fail (e.g. if you see bad sectors increasing), and even to swap them with larger ones (if you're running out of space), without any downtime.

¹ Doesn't apply to RAID 0.

Raid 1 isn't meant to protect you from deleted files. It only provides protection (redundancy) in the case of disk failure, wherein if one drive fails, the other has a complete copy of all your data.

RAID 1 consists of an exact copy (or mirror) of a set of data on two or more disks; a classic RAID 1 mirrored pair contains two disks.

This layout is useful when read performance or reliability is more important than write performance or the resulting data storage capacity.

The array will continue to operate so long as at least one member drive is operational.

^{From wikipedia}

Incremental backups, on the other hand, will help you in case you end up deleting a file by mistake, but if your main drive fails, you will lose all the data that hasn't been backed up.

It is always recommended that you use one in conjunction with another, such as by having your NAS work in a RAID 1 configuration, and then taking regular backups on a third drive (or possibly another RAID config!).

Some points the other answers have glossed over.

• A backup is a point-in-time copy of your data. A RAID1 or higher array is a right-now redundant storage of your data. So if you did a daily backup (and it completed quick enough) then you could be restoring data that is up to 24 hours out of date. Can your use-case cope with losing a day's changes?

• Cost - you mentioned in a comment that RAID1 feels wasteful. It is. But if the cost of losing your data is high enough then the cost of doubling the drives is miniscule. The cost of downtime also has to be considered.
  Would I RAID and backup my /photos directory? Absolutely!
  Would I RAID and backup my /TV+Movies directory? No, not at all.

If your budget is limited, RAID may not be feasable. However good backups are priceless. You can't replace some data like family photos, scans and documents.

TL:DR Backups are mandatory, RAID is optional.