An SCP object is classified as Euclid when its behavior cannot be unerringly predicted, either because the item is sentient, it behaves outside of current scientific knowledge, or its nature is simply poorly understood at present. Euclid-class objects do not pose the same existential threat to humanity due to containment breach that Keter-class objects do, but they still generally require more diligence to keep contained than Safe-class objects.
Although many Euclid-class objects could be used for the benefit of the Foundation or of humanity, they may have unforeseen ramifications after their use due to their unpredictable nature. Some Euclid-class SCPs are eventually understood well enough to be reclassified as Safe, but most remain inscrutable even to the most rigorous of experimentation.
Definition of EUCLID taken directly from the CSP website.