Having worked with one this summer, and questioned a number of others over the past few months, I can tell you exactly what they do. They're basically a match-maker.
For the better-known schools they act as the initial vetting provider, screening the suitable candidates for interviews & entrance exams etc. For the lesser known schools they basically help them fill up the vacancies.
I just came back from a "Education Expo" held in Hong Kong, where ~20 schools from the UK were here to recruit boarding school students. I was there for only 1 hr (expo runs for 2 days I'm told) but there must have been 1000+ parents & children present, from Y7 all the way to sixth form, all looking to secure a place at one of these schools (and yes, the schools mentioned above were present at this expo - probably why you saw "that" post earlier this week).
Education is a big business. As some have mentioned in other posts, the average UK household is no longer able to afford the day fees at independent schools, let alone the fees for full boarding, so the schools have had to cast their nets further afield to sustain their business model.
But why China or Hong Kong? China - because that's where the money is today (PM Cameron put on quite a show for Prez Xi this week, no?). Hong Kong because there is money there and the locals simply do not trust the government and the direction they are taking with the secondary syllabus.
In my experience, the very top schools (Winchester, Eton, Harrow, Wycombe Abbey, Cheltenham Ladies etc) do not have to employ agents. Their brand and prestige is usually more than enough to get oversea parents to register their child very early on. However, for those the next tier down or further below (I'll avoid naming schools least I offend any parents), they will use the agents for the reasons I've stated above.
Are they any use? From my experience, there is little value add for any parent who has done their homework. That's because those parents have probably screened a shortlist of schools and have already applied/registered with those they are most interested in. However, for those parents who have little or no knowledge at all about the UK or boarding schools, the agents are probably the best guide they can access right now, particularly if English isn't the parents 1st language (as Happy said).
Bear in mind also for DC's currently in Y8 or preparing for GCSE's, most of them would have missed the deadline for Sept 2016 entry already, so the agent is really helping them screen schools that still have vacancies available for next September (or the other way around, helping the school fill a GBP30,000+ hole in their budget next year).