A task or errand; something you have to do (often something you go out to do). More everyday and concrete than 用件.
今日は用事があって会社を早く出た。
I left work early today because I had errands to run.
子どもの用事で週末は忙しい。
I'm busy on weekends with my child's activities/errands.
今、用事で外出中です。
I'm out running an errand right now.
何か用事がありますか？
Do you need something? / Is there anything you want?