definitely，adv.肯定;没问题;当然;确实;确切地;明确地;清楚地;
例句
He's definitely giving you the eye!
他肯定是在向你眉目传情！
certainly，adv.当然;肯定;无疑;确定;行;
例句
I can certainly feel the effects of too many late nights.
我当然能感受到熬夜太多产生的影响。
简单来说就是表达不同程度的“确定”。certainly是确定,definitely是非常肯定,一个比一个更确定
definitely是确实的意思，absolutely是绝对的意思，而affirmatively则是肯定的意思，区别可以从以下例子看出：
He is definitely has competence, I believe he can beat him affirmatively, he will win the battle absolutely. 他确实是有能力的，我相信他肯定能打败他，他绝对会赢。
Certainly
这个单词用来强调和展现（说话一方）对于某件事感到毫无疑问和确信，类似“当然”。
造句范例：
I certainly never expected to become a writer.
It is certainly true that there are .
This car is certainly not mine.
对话范例：
Rose: John, I read your novel yesterday. You are such a great writer.
John: Thanks. I’m glad you liked it.
Rose: Have you always wanted to become a writer?
John: I certainly used to write a lot when I was younger. But I never expected to become a professional writer.
Rose: I must say you are doing well. You are certainly going to be a successful author someday.
John: Well, there’s certainly a long way to go. Can you help me to improve?
Rose: Certainly.
Definitely
这个单词可以被用来表述自己明确的态度，完全的同意或是强烈的肯定，类似“确实”。
造句范例：
I definitely need a holiday.
I think iPhone6 is definitely bigger than iPhone 5.
The hotel fitness centre is definitely worth a visit.
对话范例：
Rose: John, did you call your mother?
John: Not yet. I’ll definitely call her in the evening. I’m sure she’s fine.
Rose: I’ll most definitely not accept any excuse this time. I want you to call her right now.
John: What’s the hurry? I told you I’ll definitely do it once I’m back from work.
Rose: Your relatives are coming over. They’ll definitely ask you for some news about her. Don’t you think calling her back is a good idea?
John: Definitely.
Absolutely
这个词用来表述绝无例外的意思，或强烈地表示绝对赞同的意思，类似“绝对”。
造句范例：
He made his reasons for resigning absolutely clear.
Are you absolutely sure?
This cake is absolutely delicious.
对话范例：
Rose: I absolutely want to do this, John.
John: Do you have any idea of what you are saying? Why do you want to resign?
Rose: I think I’ve made my reasons for resigning absolutely clear.
John: I understand your reasons, Rose. But we had been considering you for a promotion.
Rose: I absolutely understand that it will be a great loss for me to leave at this point. I just can't stay any longer.
John: It’s your final word then.
Rose: Absolutely!