Unlike Windows, in Linux there are multiple partitions mounted to
directories under the root /. Linux partitions and device mounts look just like directories, and that is done on purpose. So, instead of having D or E drives you have things like /media/CDRom, which in my opinion makes a lot more sense than E drive. Even shared directories on a network look like they are just part of the normal directory structure.
On a home computer install, you may or may not have multiple partitions off of the root /. However, it is very common to have multiple partitions off of the root / on a Linux server in order to isolate those partitions from each other and from the root /. For example, you wouldn't want a ton of logs for some application to eat up all of the disk space and affect the space available in users' home directories. Creating partitions guards against that kind of thing. And even if you have a home Linux install with only a single root / partition, you will still have directories that exist which are named after common Linux partitions.
Some common Linux partitions are as follows.
/home - user account directories
/var - FTP, web server, mail, etc.
/tmp - temporary files (e.g. when you open a file in a text editor like vi)
/boot - boot partition, you know, for booting the OS
/usr - applications and utilities
Some common Linux directories are as follows.
/etc - configuration files
/bin & /usr/bin - common executables
/sbin & /usr/sbin - admin executables
/opt - third party applications
/var/log - various system logs
The Bottom Line
Linux partitions help guard against the possibility of problems, such as one partition bleeding over into another. They allow administrators to make certain assurances about the system (e.g. users can't fill up the root / partition). On a home computer, you might not need, want or care about several different partitions. But you should at least know about them and what they are used for.