What is a Saint's Day actually the anniversary of?

Typically, they are observed on the holidays of the people the christians conquered. A little tactic to partially incorporate native religions into the fold by renaming their deities as saints and repurposing their holidays as saints days, thus the people continue worshiping their own religion in secret, but a few generations later their children have no idea any religion other than christianity was ever involved. Examples include St. Patrick's Day, Christmas and Easter.

Traditionally a saint's day is the day of his death.

Satan's birthday -.-

You mean All Saints' Day. It's not an anniversary. It's in honor of the Catholic saints who didn't make it on the liturgical calendar. Saints are commemorated on every day of the year.

Originally, only martyrs were made saints, and the saint's feast day was the day he or she was martyred. The tradition continued, with non-martyrs feast days still being their death dates.

As there became more and more saints with feast days, steps were taken to try and avoid duplicates, so feast days were named NEAR their death dates, but not precisely on them.

One reason there was argument among early Christians about even celebrating Christmas was because it was viewed as traditionally pagan to observe a deity's birth date - Christians observed martyrdom instead.

There’s a calendar made that every day there is a saint that died which is assigned to the day you are born. At childbirth, supposedly that child is already assigned a saint.

All the Saints who numbered beyond 365 had to have a day ( !0/31 ) to be celebrated ; probably so they wont haunt the Trick or Treaters .

Most saint's days originally **commemorate the saint**.

They typically are not on the anniversary of any particular event, nor are they intended to be.

- Note that the same can be said for Christmas. It is the day that, traditionally, the birth of Jesus is celebrated, but it is NOT the anniversary of the date of Jesus' birth.

Some saint's days commemorate a particular event in the saint's life (again, similarly, Christmas), but that is the exception rather than the rule.

Your birthday.

The feast day is generally the day the particular Saint died but if day of death is unknown the church just assigns a date on the calendar

For example Saint Valentine was martyred on February 14th (which became Feast of Saint Valentine) aka Valentines Day

https://en.m.wikipedia.org/wiki/Calendar_of_saints