What you are seeing is a little misleading, because most of those lines aren't real partitions.
The line with filesystem udev is a virtual filesystem that does not exist on disk, and just represents some data in memory.
Lines with filesystem tmpfs are virtual filesystems that exist only in memory, or swapped to the existing swap partition. They are not from actual partitions on the disk.
The line with filesystem cgmfs also appears to be a virtual filesystem related to the cgroups manager which you have for some reason.
That leaves only three lines referring to actual partitions on the drive: partitions
sda5 contains your entire Ubuntu install, is 69GB and is mounted at
sda3 is your Snow Leopard (Mac OS install) which is 55GB and mounted as an add-on drive in
sda2 is another partition which is 19GB and is entitled "LINUX". I don't know why you have this partition. It's possible you created it intending for it to be your Linux partition (maybe for a previous Linux install) but you ended up not using it. It's basically empty.
When you install something in your Ubuntu installation it'll go into that 69GB