You screwed up. You know that, so that's a good first step. I agree with Joe S on the first thing to do: tell them honestly what you did.
But to go forward, you need more than that, since this wasn't the first kind of problem related to your communications (and this certainly is, as your question suggests). You need to show that you are going to fix this.
What kinds of things do you do to proactively prevent this from being a problem, in the future? Come October 12, let's say you accidentally think it's Thanksgiving (perhaps you're Canadian) and don't come in to work. What can you do, now, to make that less likely to happen, and less of an issue? Here are some suggestions, but you should do whatever fits best in your corporate culture.
- Tell your coworkers how to contact you, outside of work. Cell phone, text, whatever. Hopefully they already know this, but make sure.
- Use the calendar feature in Outlook (or whatever you all use internally), and use it for everything. Put all of your time off in there, even if it's just an hour or two. And even if it's a holiday. Then share that with the office.
- Send out "time off" emails. Email the folks that you would expect to communicate daily with (or weekly, if you mostly work alone) a few days before every time off, to let them know how to contact you or who else to contact during your time off.
- If you have status meetings, mention time off including holidays during each one, up to the next one.
Whatever mitigation options you can come up with - mention those in the email. (And do some of them first, before you send the email, so it's not just "promises" but real action.) Send the email to everyone that was affected by it, not just your manager.
Here's an example.
I was out Friday due to a confusion as to what day Labor Day was. I'm very sorry that I got that wrong, and didn't double check which day it was. I hope that it didn't cause too much difficulty for anyone, and I'll do my best to fix any problems that came about as a result so that my absence won't cause any significant delays or issues.
I have updated my outlook calendar with all time off, including holidays, based on the corporate calendar available [here]. I will keep this up to date in the future, so that this kind of mistake doesn't happen again, and to make it easier for you all to know where I am.
If ever I am not in the office and you need to get ahold of me for any reason, you can call or text my cell at (555)555-5555, or contact my manager, Jane Black.
Again, my apologies for the mistake. I will do better in the future.