Travertine tiles are made of cut stones produced from deposits of hot spring limestone. It is widely employed in walls and floor tiles due to its enduring character.

While travertine tiles do not get damaged quickly in a moist setting overexposure can ruin it.
Water resistance:
As with any other porous rock, travertine is capable of holding water.
Taking outdoor travertine pavers to the swimming pools should be avoided for those who use salt pools.
What sealing does is that it prevents the absorption of water, therefore sealing also protects the appearance and durability of the stone.
Water damage:
When a surface is damp for an extended time, staining, mold, and erosion might start to occur.
Polished travertine surfaces can be particularly treacherous when wet, as they can become very slippery.

With adequate care, travertine tiles can last for decades. A majority of individuals appreciate the weathering effect that occurs over time, and for those that desire to halt it, the tile can be maintained in the condition it was set in.

You need sealing because the stone is porous. If not sealed, porous stones will absorb moisture, water, and any spilled liquid, causing stains and etching marks which would deface the stone’s natural beauty.

Here is a question that has been out there forever: is it possible to apply a tile without grout? In summary, it is not recommended that tiles be set without grout.