You have full disk encryption turned on, and your Disk Utility does not have Debug > "Show All Partitions" checked, so, it's a little confusing, not the whole picture.
With the "Show All Partitions" turned on, you will see something like this:
As Toutou said, the first line is the physical drive. Everything under it are the partitions that are on the drive. EFI is the "BIOS"-like boot functions for the machine, "Recovery HD" is for system recovery. Note, there are two "Macintosh HD" items. When the disk gets encrypted, you get a partition type listed as "Core Storage Physical Volume" that is about the full size of the disk. That's the encrypted partition/drive. When you start the computer, that encrypted glob of data gets decrypted and turned into the second "Macintosh HD" you see. Think of that second volume as a "virtual drive". That drive/volume/partition expands and contracts within the size of the encrypted disk and gets re-written to the core storage (encrypted) volume.
So, there is room to write data to "disk", it's just that you are dealing with partitions and having a level of indirection going on to deal with the encryption. Basically, the physical drive is full of encrypted storage, hence, why the drive shows a "full", when the computer's partition really isn't full.
ADD: to get a better idea of how this all lays out, and imo, a better representation than Disk Utility, bring up a Terminal window and issue the following command: diskutil cs list
OH AND: is it possible the memory message is referencing RAM vs disk? Depending on apps running, some are not very good at freeing up memory. Some, especially if running a while, are plain old resource hogs (browsers, especially with lots of tabs open). Fire off "Activity Monitor" in the Utilities folder (under Applications) and click the Memory tab to see if your RAM is busting at the seams.
