Would a powered USB hub solve the problem of two external disks randomly losing connection or being slow? I have an older MacBook (circa 2012) and I have two external drives. I want to merge the content of the two drives but Finder is having fits with it. It will lose the connection to the drives at random times and otherwise do transfers very, very slowly (like an entire day for a modest amount like 500MB)

The external drives are not powered and I only have one USB port on my MacBook. The USB hub is nothing special, rather basic really, but everything I'm using (including the cables) claims to be USB 3. I am starting to wonder if the hub is the weak point in my process and perhaps I need something else. 

Would a hub that has its own power help in this scenario? I guess I've never really understood the differences between a powered hub and one that is not.
Yes.  A powered hub would definitely help.

The USB port on your MacBook Pro puts out 5V @ 500mA.  Now, remember, every device you hook up to that port will require some amount of power, including the hub.  

External hard drives use about 2 to 2.5W of power.  Using the formula below to get calculate Amps,

Watts = Volts x Amps


We can see that an external drive uses from 400mA to 500mA.  You’ve got two drives plus a hub so, it’s easy to see how you could quickly oversubscribe the power available.

A bus powered hub (what you have) gets its power from the host, in this case, your Mac.  A powered hub, in comparison, supplements additional power, sometimes up to 3A (depends on the hub) so you can drive more devices without oversubscribing the bus power.