The CEO is the highest ranking person that works at the company every day. The board of directors can fire the CEO, but the board usually meets only quarterly and its members usually have other jobs.
A CEO’s day to day will depend on the size of the corporation. Generally, they are responsible for hiring and managing all of the other executives. So they might hire the head of product development, head of sales, head of marketing, general counsel, chief financial officer, and more.
It’s their job to attract good people into those roles, then motivate them to do a good job. All of those folks have different areas of expertise (sales, legal, accounting, engineering) so they need to listen to their expertise and then decide a plan for the company based on that.
For instance, the CFO can tell them how much money they have in the bank, and the CTO can tell them that investing an extra billion dollars in R&D can produce a product that will increase revenues by an estimated $100m/year after 3 years.The CEO needs to decide whether they can afford that, whether they believe those revenue projections, and whether the new product would be an overall positive direction for the company.
When the company has a really bad year, they need to figure out what needs to change: do they need to fire and replace some of these executives, change company culture, cut some of their product line?
All the decisions are ultimately either up to them, or up to people that they hire and trust to make those decisions.