Grubbers are a race of subterranean creatures currently lurking in the ruins and Catacombs beneath Marcuria. They are not actually named in the game - their name is given on the Dreamfall website and promotional material.
They come in two kinds. The first are "New" Grubbers (given this adjective in the Concept Art) who wander the ruins, carrying lights or just watching the floodwater in the cavern. They wear only a ragged loincloth and carry staves. Their behaviour is not consistent - when Zoë Castillo encounters them, they attack her, but April Ryan seems to frighten them away. The second are larger "Warrior" Grubbers who are summoned by normal Grubbers when they are afraid, and dispatched as guards or foot soldiers by the Prophet. They are heavily muscular, capable of killing a human in a few blows, and have sharpened teeth. The implication of the differing adjectives may describe an evolution (or devolution) of the Grubbers, from Warrior to "New".
Zoë is shocked and confused by these Grubbers, wondering if they are "Ape? Human?" When April follows the Prophet into the caves, she sees one of them sing to the doors in the ruins to open them with magic; when she returns to the surface, Na'ane reminds her of the 'earth-singing' magic of the Banda and ponders if they could be related. Statues April finds in the Catacombs seem to remind her of the Banda - they might represent a common ancestor between the Banda and the Grubbers, much as the Maerum and the Alatien once had.
The four-note melody that appears in puzzles down in the caves seems to have some significance to the Grubbers. If Zoë uses stealth to evade the second Grubber, leaving it peering down into the water near the Catacombs, it can be heard humming the melody (though not very clearly). This might be simple imitative behaviour, given that the notes form the core of several puzzles down in the caves, but as the Grubbers seem familiar with the melody, it may have originally been part of their culture.
Reassuringly, a disclaimer at the end of the credits states: "No Grubbers Were Harmed In The Making Of This Game."
Said at 03:17:00 twitch.tv livestream : Dag: "we never really expanded their story". Ragnar: "that will be continued in Dreamfall Chapters.." Dag: "yeah, they’re important", Ragnar: "because these things are very central to what’s happened here, yeah. They’re linked to some of the events that go on above ground. But I can promise you that you’ll not be FIGHTING any grubbers in Dreamfall Chapters!"