If I connect two usb drives to an external USB hub and I copy data from one drive to the other, does the data go through computer? Or will the data be managed by the USB hub?
Does this have some performance benefit?
No, this won't work. All data you are copying will need to be read by the computer from the source drive, before they are copied to the target drive.
If anything, having two hard drives connected to the same USB hub might slow things down. If you have multiple devices connected to the hub, they have to share the bandwidth.
USB are a host-driven protocol, not a peer-to-peer standard like firewire. Drives are just devices, they're not host to control or decide anything. Without the host they cannot even interact with the outside world.
Assuming that you can connect the two drives like that, how can they know which files/folders you want to copy? Will they copy from which drive to which drive, and will they overwrite duplicated files? How will they behave if the drives are full?
Devices connected to the computer through a hub can't talk to each other or share data within the hub; all traffic is between each device and the computer.
There is no performance benefit from connecting two drives to a hub, and there may be a performance detriment. The hub, itself, is connected to the computer through a USB connection, so everything connected to the hub has to share the capacity of the hub's computer connection.
Concurrent use of more than one drive connected to a hub as USB 2.0  will generally exceed the USB 2.0 bandwidth of the hub's computer connection, potentially also affecting the performance of other USB 2.0 devices attached to the hub. This can happen even with a single USB 2.0 connected drive while actively transferring data.
 USB 2.0 connection includes USB 2.0 drives connected to any hub, or USB 3.0 drives connected to a USB 2.0 hub. On a USB 3.0 hub, USB 2.0 devices have a separate USB 2.0 data path with its own bandwidth limitation.
USB has what is called a tier star architecture - there needs to be a master who is the "real hub". The master sends out tokens giving the devices chance to send/receive. So there is no h/w bus contention like in other buses (remember 2 wires only).
So there is no device to device transfer - you have that on SCSI or 1394 (firewire) - one reason they are lot more expensive and complicated to do since everyone must be capable of being a master during arbitration.
So data transfers are always between the master (usually hosted on a computer) and connected devices. A devices does not even know of the existence of the other devices. Hub is just another device with special characteristics.
To answer the title question, there is USB On The Go, so theoretically, yes. A phone connected to a hub connected to a flash drive can read data from the flash drive without needing a computer to actually perform the data transfer.
In practice, what you really have there is a device that is actually a host.
Also, only very few device support that, and typically no drives that I know of.