Firstly, they look after the interests of Brits in China: registering births, marriages and deaths; dealing with custody cases, arrests and emergency medi-vacs; lost passports; problems problems problems... One of the first things I saw was a bullet-proof counter for difficult cases and a Tea & Sympathy Room for grieving relatives. One has to be pretty hardened to work here.
Secondly they process visa applications for Chinese wanting to go to the UK. Over 1,500 a day! There are trolleys and boxes full of passports & paperwork and scores of people beavering away at verifying them. They're turned round pretty quickly and the rejection rate (less than 5%) is lower that one might think.
Do they ever get thanked for what they do? Very rarely I should think.