Hard drives connect to the computer using a connection called "IDE". This connection allows for two hard drives per connector. The main drive is called the master drive and it is the drive your operating systems runs off of.
The second drive is called the slave drive. Your computer can't start off of this drive, but it can use it for storing information.
Normally, you need to tell the computer which drive is the primary drive (master) and which is the secondary (slave). That is what they mean by setting the drive as a slave.
It is straightforward to set up a second drive as a slave drive and configure your computer to use it, but you do need some knowledge to do it. There are a lot of resources on how to do this, but if you don't feel confident about doing it, a local computer shop should be able to help you purchase the new drive and then install it for you for a very fair price.
Your data will not automatically synchronize to the new drive. You will need to either manually back up your data or set up some software to do it for you automatically (preferred). The computer shop should be able help you select an appropriate software package and help you configure it.
There is another option, configuring your system for RAID 1 or mirroring. This would make an exact, essentially invisible, copy of your main drive. You would not be able to use the second drive for anything else and it is significantly more complex to configure and restore from this configuration. You can look for more information about this online, but its probably overkill for your situation, both in terms of function and complexity.
Good luck!