Oh well, I should have googled “etymology aujourd’hui” myself. From Wiktionary I got this answer,

au +‎ jour +‎ de +‎ hui, literally “on the day of today”; since hui
comes from Latin hodie, the phrase literally means “on the day of this
day”.

To add to @grokus answer, we need to write that apostrophe because that is the rule with that préposition when it stands before the h which is muet.

You may be interested to read Comment distingue-t-on un “h” aspiré et un “h” muet ?