Very little in terms of day-to-day, unless a board director decides to make it his/her mission to change something at that very low level. The board meets typically quarterly (monthly depending on the circumstances?) and is generally focused on higher level questions like the company's growth trajectory and forecasts, major problems, compensation strategy, hiring key executives, fundraising, M&A, etc.
Like I mentioned, any board member can decide to make an issue out of something, but you would expect a very legitimate reason to waste the other board members' or executives' time with a nit about a specific product feature or marketing campaign. Not to mention, a board member that meddles too much in the daily affairs of the company would draw scrutiny from both the CEO and other board members for not focusing on important strategic topics.