Embedded calendar events

The only system-default calendars you mind find on your iPhone are Holidays, Birthdays and Siri Suggestions.

If you don’t want to see any of it, open the Calendar app, then tap ‘Calendars’ button, and on Calendars list screen look for and toggle off those you wish not to see it. Holidays calendar, if available to you in your region, will have ‘i’ button next to it name where when you tap on it, you will get an option to toggle off Event Alerts for that calendar.

If you did the above, and you still see some events that shouldn’t be there, you have other calendar account the events are stored on. You can check what Calendar accounts are added by reviewing accounts under Settings > Calendar > Accounts, where you’ll get option to simply turn off the Calendar option on the account or delete the account altogether.

What do you mean by "embedded?

Tap on the event. Go to the bottom of the page. Tap "Delete Event".

If you don't want to see a holiday calendar, tap the word "Calendar" at the bottom of the screen while in the Calendar app. Untick those calendars you don't that you don't want to see.