Eventful things are exciting, important, or full of incidents. Your eventful life might inspire you to write a fascinating autobiography one day.
If your day is eventful, a lot of things happen — it can be good or bad, but it's certainly not boring. If you see a hot air balloon land on the highway while you're driving to work, and when you arrive all of your co-workers are wearing costumes, and then your boss gives you a huge raise, you can call it an eventful day. The word dates from about 1600, meaning literally "full of events."