The term storage media refers to any number of objects - CD, DVD, USB flash drive - basically any device that can have any form of data stored on it.
When deciding where to keep your data, remember that everything rots, and everything breaks down. It's the way the universe works, and there's not much we can do to stop it. Therefore, you have to think about your data's lifetime in terms of months, years, or decades.
Very little data most people have truly needs decades of preservation, but often, it doesn't hurt to have it around as long as possible. A minor amount of effort will help mitigate that. Specifically, expect to renew/refresh your data storage every 3 years or so - anything you don't do this with will progressively be subject to bit rot, moisture and heat damage, and being shoved into progressively unpleasant locations at home and office before someone decides it's trash.
More information about bit rot can be found on the Wikipedia article.
Compact Disks, Digital Video Disks, High Definition DVDs (HD-DVD), and Blu-Ray (BD) are all optical media. This means that information stored on them is read by a laser. It is debated how long the shelf lives of these products are, while commonly accepted that DVDs have a shelf of 20 years, and CDs have a shelf life of 3, it is unknown obout the others (some of these technologies haven't existed long enough to know this). http://www.forensicswiki.org/wiki/Category:Disk_imaging contains some info on retrieving data from them; ISOdisk is a good tool for Windows. See also .
Compact Disks (CD)
Professionally produced CDs (such as those you would by from a store) are accepted at having a shelf life of up to 7 years. CD-Rs and CD-RWs, however, have a shelf life of only about 3 years. They store only up to 700 MB and have only a single layer. Not recommended by today's standards.
Digital Video / Versatile Disks (DVD)
As with CDs, DVDs that are professionally produced have a longer shelf life than recordable ones, although there is less agreement as to how long they last. 4GB on a single layer, double that on a dual layer. Generally not recommended as much as hard drives by today's standards (unless you can't use your hard drives for whatever reason).
High-Definition Digital Video / Versatile Disks (HD-DVD)
HD-DVD (Toshiba, mainly) is dead and buried, having lost the format war to Blu-Ray (Sony). It is recommended that you back up any data on an HD-DVD and transfer it to another format. You probably wouldn't be able to find any empty HD-DVD disks to use for archiving, so don't try.
So named because of the blue laser needed to record and read a Blu-Ray disk, Blu-Ray is the newest optical media available. A normal Blu-Ray disk is able to store 25 GB on a single layer, or 50 GB for a dual layer (new standards from Sony have up to 300GB of space however). However, Blu-Ray is also the most expensive backup format available, and with no available information on shelf life, is not recommended.
Hard Disk Drives (HDD)
There are many forms of hard drives, including internal hard drives for laptops (2.5") and desktops (3.5"), and external hard drives that can run free of a computer. While external hard drives fall under the replace-every-few-years rule, data can be bought cheaply in comparison to other formats ($80 could probably buy two terabytes of storage), and so are the recommended format used for backups.
External Hard Drives
These are regular internal drives fitted into an enclosure, usually with a USB cable for connectivity. Functionally, they are more or less like using a thumb drive. Externals are quite cheap these days, and can be bought for as low as $80 and $130 for a 2TB and 5TB respectively. For a bit more, you can buy drives with smaller form factors and USB power. They're a very affordable way to keep your data backed up.
Network Attached Storage (NAS)
Unlike external hard drives which are dependent on a host PC, a NAS is more or less its own computer. They contain slots for one or more HDD (or come with them built-in), an ethernet port and such basic features as print server, file server, BitTorrent client, etc. This allows them to function independently of any PC, allowing any computer on the network access. A good NAS will set you back $150 or more depending on available drive bays, bundled drives and feature set.
Hard Drive Docks
HDD Docks are essentially enclosures for multiple HDDs. Like an external hard drive, they usually connect to a single computer via USB. Lacking the fancy features of a NAS, they can be significantly cheaper, and have the advantage of requiring only one power socket and USB cable for multiple drives, as opposed to the requirements of a legion of individual externals.