In my business, to over-deliver means to me that -
1. I am consistent: this means showing up by replying emails, posting on your threads and just being generally accessible by those who rely on you for one service or another.
2. I have integrity: meet deadlines (beat them in fact). Don't promise one thing and deliver another. Be on time. If you can't meet a stated deadline (and you should), be upfront about it.
3. I will deliver quality: this is really important because it's what keeps people coming back. Quality. Never compromise on it.
I've probably left some stuff out, but what does that word 'over-deliver' mean to you?