I have no idea what the board on the left does. It is a small piece of PCB with a ZIF socket mounted on it with three variable resistors of the type you turn with a screwdriver. It is a complete mystery to me.
I think I have identified the board on the right using my fine powers of deduction. I have worked out that it is a chip tester. I deduced this by reading the words "CHIP TESTER" on it.
The long IC in the middle is a 6522 like the system and user VIA inside the BBC. There is a socket on the left with two rows of pins on each side to take the smaller chips as well as EPROM-width devices. There are two ribbon cables, one ending in a 20-way socket, the other 34-way.
I have found a software disc. The idea is that you plug in a chip, tell the programme what you have put in and it will test if it works. I did try this but it said to turn the Switch to 18 but it did not appear to have a setting for 18.