There are many things you can say. This type of question doesn't have a wrong answer. All answers will be correct. So the best answer is how good you can make the answer. A mediocre answer will be something like completing a project on time. You can say this, but add another twist to make the answer a little better. Here is an example.
Short Answers :
"To me, success means to have a goal, plan the steps to achieve the goal, implement the plan, and finally achieve the goal."
"Success means to produce high quality work before the deadline."
"Success to me is knowing that my contributions positively impacted my company."
Long Answers :
"Success to me means completing a task and when looking back, thinking I couldn't have done it better. To succeed is to complete a task or assignment on time in an excellent manner. But that's only half of it. The results should be good and the people involved should gain a valuable lesson or experience. For example, if it was a group project, and only two people out of four really did the work, I wouldn't call that success. If everyone participated and worked together providing a valuable deliverable then it's a success. So I think both the result and the process should be great to call something a success."
This answer is showing that you believe in delivering great quality work. Moreover, it is implying how much you value team work. If you value teamwork highly, then it is safe to assume that you would make a great team player.
This is a good question to highlight your achievements. Don't be smug or arrogant about the success of a project, especially if it was a team effort. You need to give credit to the team, too. You could say what you contributed to the total project and also give credit to others that helped in your success. Don't be overly modest, either.Here are some pointers:
1. Pick something that was clearly a success and highlight your skills.
2. Pick something recent. If you pick something twenty years ago, they are going to wonder what you have done lately.
3. Pick something important. You may have succeeded in many projects that are not that significant.
4. Pick something easy to explain. If complicated, give the short version.
5. Be sure to explain what you learned from this success.