With previous releases of the VCSA, increasing disk capacity was not a very straight forward process. Even though you could easily increase the size of the underlying VMDK while the VCSA was running, increasing the guestOS filesystem was not as seamless. In fact, the process was to add a new VMDK, format it and then copy the contents from the old disk to the new disk as detailed in VMware KB 2056764. This meant with previous releases of VCSX 5.x, you would need to incur downtime of your environment and it could be also be quite significant depending on your familiarity with the steps mentioned in the KB not to mention the time it took to copy the data.
UPDATE (12/06/16) - For VCSA 6.5 deployments, please refer to the article here as the instructions have changed since VCSA 6.0.
The reason for this unnecessary complexity is that VCSA did not take advantage of a Logical Volume Manager (LVM) for managing its disks. In VCSA 6.0, LVM is now used to make it extremely easy to increase disk capacity while the VCSA is running. VCSA 6.0 further simplifies this by separating out the various functions into their own disk partitions comprised of 11 VMDKs compared to the monolithic design in previous VCSA releases. This not only allows you to increase capacity for specific a partition but you can also now attach specific storage SLA's using VM Storage Policies on specific VMDKs such as the Database or Log VMDK for example.
In the example below, I will walk through the process of increasing the DB VMDK from the existing 10GB to 20GB while the vCenter Server is still running.
Step 1 - Verify the existing disk capacity using "df -h"
Step 3 - Once the VMDK has been increased, you will need to run the following command in the VCSA which will automatically expand any Logical Volumes that have had their Physical Volumes increased:
vpxd_servicecfg storage lvm autogrow