Here's how it goes. Partitions is physicaly divided space on your harddisk. A quick analogy to Windows as this is more easily understandable to people. In Windows, you have C: and D: and E: . These are partitions. Now you can imagine your harddisk being split in three pieces(it is not, it's just virtually divided). Partition is a virtually divided space on your harddisk. You can split an 80 GB harddisk into smaller partitions, like C: (20GB) D: (15GB) and E: (45GB). Now this is all the same in linux. Just that here partitions are identified by /dev/hda1, and /dev/hda2, and /dev/hdb1..... All you have to do is take the /dev/ part away and you can easily say where and what partition that name refers to. hd stands for hard disk and a stands for primary harddisk, and b stands for secondary harddisk.
So hda would be your primary harddisk
and hdb would be your secondary harddisk (presuming you have two harddisks in your computer)
now hda1 would mean that you are refering to the first partition on your primary harddisk (if you have windows on your computer, this would be C
hda2 would be the second partition on your primary harddisk and so on.... You get the idea?
Mountpoints in Linux is where the partition is mounted(like pluged in). If you mount your 3rd partition to /home then all the files in /home are from that 3rd partition as only one partition can be mounted on the same directory. However you could mount another partition on like /home/someotherpartition.
The easiest way to determine what belongs to what partition is to issue a mount command, which will tell you what partitions are mounted and where.
Oh and if you are rebuilding from scratch, just don't touch the partition you want to hold for the new install and just mount it where you want later, whern you are finished with installing.