Full details on their website in the penultimate heading on this page.
I saw a hair pulling-out discussion of the fairness or un-PC-ness of this on another site. A lot of the arguments were also about Mother & Baby magazine's initial reporting of this which incorrectly said it applies to all National Rail travel.
Personally, I think it's great news that the system exists on at least one rail service. At the same time, it's a pretty sad state of affairs that we still have to have notices around asking people to give up seats to pregnant women and others who look like they need a seat more than you.
I know there's a number of people who don't look like they need to sit but have various conditions which makes standing difficult, but that doesn't apply to 90% of people in carriages. I know a number of us have our heads in papers and genuinely don't see pregnant women getting on trains - but again that's not 100% of the carriage. I know people worry about offending women by offering seats - but I'd rather risk offending someone and offer a seat. I don't look pregnant but occasionally (and I mean very, very occasionally) get offered a seat just because I'm a woman and I don't see it as offensive or that years of Women's Lib has been thrown out of the window. However, that doesn't mean I think it's a god given right for all women to be given seats.
It may just be the carriages that I'm on, but I find it's usually other women that offer seats to those pregnant or the elderly (male or female) and they're not prompted to do this because the pregnant one is wearing a "Baby on Board" badge. To me it's just a sense of looking out for other people who might be having a harder time on the train than yourself.
Anyway, I hope other rail services follow First Capital Connect's lead and roll out this service.