Your question can be answered in at least three different ways:
1. Partition Mirroring
The SD card on the Raspberry Pi functions just like a hard drive or SSD on other systems, such as the PC.
You can build a RAID 1 on a partition that is on the SD card and some other drive, such as an external HD connected on the Raspberry Pi's USB port.
You will most likely need a powered USB hub for that. Just check the questions referring to external hard drives.
You can even plug in another SD card using a USB SD-card reader and build a mirrored partition that physically lays on the two SD cards for redundancy.
One thing you should not try to do is build a RAID 1 on two partitions that lay on the same SD card, as most, if not all, SD cards out there balance wear and this would result in a very high probabililty of failure of the two partitions in a close time proximity.
There a blog post about someone who built a similar solution on the Raspberry Pi.
2. Remote Mirroring
You can set up two different Raspberry Pis and keep a backup copy on one of them, used as a standby, using a tool like rsync and switch to the second one if/when the first one fails.
You can check an example on how to implement this here.
3. Back Up
Given that your question most likely involves keep the data safe more than having it in high availability, a good approach would be to keep a back up copy of your data.
A number of backup software are available on Raspbian package system, including simple and complex ones. Of the complex ones, I like Amanda, but Bacula is used by many too.
As for the simple ones, I suggest deja-dup, giving you the ability to store your backup encrypted on the cloud.