Reading provides a lot of varied benefits, many of which could be helpful in most jobs.

• Dealing with people -- reading (particularly fiction) can help you become more empathetic. And reading can expose you to a broad range of topics and interests, allowing you to connect with more people by potentially being conversant in (or at least aware of) their interests
• Communication -- as noted by many here, reading a lot helps improve vocabulary, spelling, grammar, and writing in general, all of which can improve your written communication. Vocabulary and some writing skills (like organizing your thoughts logically) can also help oral communication.
• General knowledge -- even if you only read fiction, you're likely to learn many facts (many authors research extensively to provide authenticity and accurate depictions of real-world elements in their fictional worlds). And of course, reading non-fiction will often provide lots of knowledge on the non-fiction topic. Having a broad base of general knowledge could be helpful in your career (even if it has no direct bearing on your job -- if it just makes the boss/coworkers think you are smart, that can be to your advantage.)
• Specific knowledge -- Non-fiction related to your field obviously is likely to be helpful to your career. And more general reading on business, success, or personal improvement can be helpful as well.
• Focus and concentration -- reading can improve these abilities, which obviously can be helpful in most types of work.
• Creativity -- Increased creativity is a widely touted benefit of reading, which can be helpful in many lines of work.
• Critical thinking and problem solving -- engaging with diverse ideas, perspectives, and arguments -- which reading can provide -- can improve critical thinking. And of course, these skills are valuable in a wide range of careers.

Obviously, what you read has an impact on how much of the different types benefits you get -- for instance literary fiction is more associated with empathy, theory of mind, critical thinking; non-fiction for directly applicable knowledge in your field or broader business knowledge. But I would not recommend putting too much focus on reading for your career -- that can certainly be a goal and an influence on your reading choices, but take care to not making reading a chore, or an (unpaid) extension of work. Get out of your comfort zone from time to time, but also read what you enjoy.

Personally, I believe that reading has helped me with all of the above, and helped my career as a result. And there may be more things to add to the list. I just went with some of the most commonly cited benefits.