“Honestly, I don't regret quitting at all.”
You got angry at your boss and quit your job a few weeks ago. You haven't found a new job yet, but you're a lot happier now. You're talking to a friend that you worked with there. He asks if you are worried now that you don't have a job. This is your answer.
Honestly, I don't regret quitting at all.
To "regret" doing something is to wish that you had not done it. It's a strong emotion, so this word should be used to describe actions that were large mistakes, not small, everyday mistakes:
I'll always regret not spending more time with my father before he passed away.
As you can see from this example, when you want to use "regret" for an action that you did not do, use the phrase "regret not ___ing".
The phrase "not at all" means really, completely none. It's a very extreme way of saying "not".
The word "not" can also be replaced by any negative word - "no", "don't", "nothing", "isn't", etc.
There was no one there at all.
I didn't say anything at all for the entire trip.
To quit a job means that you announce to your boss that you are going to stop working there.
I quit because the hours were too long and the pay wasn't that good.
This is the "normal" word for this action. A more formal phrase that means something similar to "quit (a job)" is "resign from (a job)".
When you start a sentence with "Honestly..." it sounds like you're telling your listeners a secret that you wouldn't tell other people. For example:
Honestly, I don't think I ever want to have kids:
People usually use "Honestly..." to share things that some other people would disagree with. It can help you and your listeners to feel closer to each other.'
Another way to use "Honestly..." is to introduce an idea that you just thought of that has surprised you a little:
Honestly, I don't think I even need this jacket today.