What was Bernard's Job?

Bernard was Hacker's Personal Private Secretary (PPS). Sir Humphrey was Cabinet Secretary, the highest position in the Civil Service. Bernard, while Hacker's PPS, was also known as a high-flier in the Civil Service, which means he is destined for the top of the Civil Service if he behaves correctly, as Sir Himphrey succeeded Sir Arnold, Cabinet Secretary in "Yes, Minister." This constantly means that Bernard must provide Hacker with enough information to look competant, but not divulge too much as to be seen as unsound by the Civil Service. In the books, which are, in my opinion, just as good as the series, Bernard does eventually succeed, and becomes Cabinet Secretary years later.

Bernard's official title is PPS (Principal Private Secretary).

He is in the uncomfortable position of effectively having two bosses. While his job is to assist the the Prime Minister, Sir Humphrey also has a great deal of power over his future career as head of the Civil Service.

Essentially, Bernard is an administrative assistant, overseeing the mechanisms to carry out Hacker's personal wishes, whether it is drafting speeches, putting together reports, or arranging meetings. He would oversee clerical staff who would do the actual work, which you don't generally see because it would probably be too costly. He would be part of Hacker's inner circle, privy to confidences that other staff wouldn't. However, Humphrey is head of the Civil Service, with power over promotions and pay increases. As such, he has a lot of influence over Bernard, though Bernard can counteract some of that, via his direct conduit to the Prime Minister.

In the structure of the show, Bernard is essentially there to ask questions for the audience, and to occassionally throw a dramatic wrench in Humphrey's schemes, by providing vital info to Hacker. He also gets to deliver many of the best punchlines. He's kind of the balance between Hacker and Humphrey.

"Fortunately, Ah keep mah feathers numbered for just such an emergency!"

I believe he would classify as an "Executive Secretary" to a CEO for the most part, though in this case, he also is beholden to other interests for longer-term advancement once the PM changes.

You can get a better look at what the job entails via the BBC version of "House of Cards" if you're interested. It's on Netflix (along with the excellent American version) as I write this...