I've noticed that a few creatures have the "titan" tag (here's a D&D Beyond search) but I'm not sure what that tag means.

I noticed the other day in my Monster Manual when looking at the Empyrean and wondered if it had anything to do with titans of Greek mythology (since that's what the Empyrean makes me think of) - but then the Tarrasque is also listed as a titan, so there goes that theory.

I wondered also if it's to do with their size, since the Tarrasque is extra big, even for a Gargantuan-sized creature, but then the the Empyrean and a few others are only Huge, not Gargantuan, so that doesn't make sense either.

I have not seen this tag defined in the Monster Manual, only a small section on "tags" (link to basic rules, listed below all the creature types) that basically says that tags don't mean anything. But even if there are no "rules" about titans, the term must still mean something, like how the "demon" or "shapeshifter" tags still mean something in-universe, at least.

Have I missed something? Although I accept that there are no "rules" about titans, there must still be mention of it somewhere as to how a "titan" creature is different from a non-titan creature. Is there any other official description of what this tag means?

What does the "titan" monster tag mean?

The DMG provides insight: they are divine creations.

The DMG states on page 11 (emphasis not mine):

Quasi-deities have a divine origin, but they don't hear or
answer prayers, grant spells to clerics, or control aspects of
mortal life. They are still immensely powerful beings, and in
theory they could ascend to godhood if they amassed enough
worshipers. Quasi-deities fall into three subcategories:
demigods, titans, and vestiges.

[...]

Titans are the divine creations of deities. They might be
birthed from the union of two deities, manufactured on
a divine forge, born from the blood spilled by a god, or
otherwise brought about through divine will or substance.

Examples for titans (or rather: all that are currently published) are the Empyrean, Kraken, Tarrasque (all MM), Astral Dreadnaught (MToF), Slarkrethel (Storm King's Thunder), Atropal (Tomb of Annihilation) and Juvenile Kraken (Ghosts Of Saltmarsh).

I'm not aware of any mechanical implications of being or interacting with a titan, except that you're probably gonna have a bad day if you mess with them. But then again, if you fight gigantic monsters like a Tarrasque, it's kind of on you if you get crushed ^^

The "titan" tag indicates a creature with divine origins

The Dungeon Master's Guide has a sidebar that briefly explores "divine ranks" on page 11, which says of titans:

Titans are the divine creations of deities. They might be birthed from the union of two deities, manufactured on a divine forge, born from the blood spilled by a god, or otherwise brought about through divine will or substance.

So the titan tag simply denotes a creature which was directly created by or from a deity in some way.

It seems like this designation doesn't necessarily extend to descendants of such a creature - Rocs, for instance, are described in the MM's text as "Sky Titans" because of being originally created by the giant gods as servants for giants, but don't have the titan tag in their stat block.