What was this sound in Minecraft?

In this situation, the cave noises; cave13.ogg and cave17.ogg played at the same time.

Cave noises occur when there's a location with a low light level nearby the player.

Although they sound threatening, cave noises are just atmospheric sounds, they won't harm your player in any way.

As these sounds are purely atmospheric and random, they also don't hint at locations to certain underground structures, resources, or mobs contrary to some people's beliefs.

Hopefully this is helpful in explaining the cave noises, and helps to relieve some fear about them.

Edit: I made a mistake in which I thought that Dan was near a cave entrance in that part of the video, which watching it back is definitely not the case, though he's in an mountain biome; which tends to have many near-surface caves, so caves sounds playing where he's at is still a very likely possiblity.