せいで is used when you want to say that something happened because of a particular cause, and that cause is seen as the reason for a bad or unfortunate result. It often carries a sense of blame or regret. For example, if you're late because of heavy rain, you might say 雨のせいで遅れた. Note that せいで is not used for positive outcomes; for those, use おかげで. In conversation, you'll hear it when someone is making an excuse or complaining. It's perfectly natural in everyday speech, though it can sound slightly accusatory if you point out someone else's action as the cause. In writing, it's also used, but keep the register in mind—it's not formal.