So I'm assuming you understand what is meant by surface area to volume ratio? (if not let me know and ill explain!)
It just means that there is a greater surface that the substance can diffuse across, and so that means more of the substance can diffuse per unit time, hence increasing substance exchange.
Say you have a surface that a substance can exchange across, if that surface is 2cm^2 (for example) then you can only exchange across that area, but if you increase that surface area, then you can exchange across a greater surface, so if this was sugar going across, instead of 1g/sec (just arbitrary number) then you might have 15g/sec which is 15x as quick! These numbers aren't exact they're just a demonstration.
Does that make any sense? I apologise!
I do not know if that helped or made it even more confusing, but I hope it helped somewhat.