The three I've heard of in concrete terms are (1) product decision making, (2) network and intros, and (3) operational focus.
1) is the partner who can help you figure out which features you'll need to go up market and hit the next stage of your growth.
2) is the partner who knows everyone and can open doors to sales counterpart and key hires.
3) is the partner who's a numbers guy through and through, and help you avoid operational pitfalls.
If it's not clear what a VC partner is bringing to the (board room) table, then it's worth seriously considering whether it's correct to take their money. Sometimes you have no choice. But if you have a choice between cheaper money and a great value add partner in the above mold, I've almost never been told to take the cheap money.
If you know of other "value add" archetypes, I would love to learn of them.