Celtic is a category of European languages which had close contact with Germanic languages. The original inhabitants of England were Celts, before the coming of the Anglo-Saxon (who spoke Old English).
Tolkien's legendarium has mainly Germanic and English elements, but Celtic concepts are present in some views about the Elves (see Elves#Celtic influence). George Allen & Unwin also criticized The Silmarillion as being obscure and "too Celtic".
Celtic analogies with peoples are present mostly relating to Pre-Númenórians, especially Dunland and the Stoor hobbits, which is evident in placenames such as Bree and the personal names of the Bucklanders.
It is possible that the rivalry between the primitive Dunlendings and the blonde-haired, pseudo-Anglo-Saxon Rohirrim who migrated into the lands neighboring them was meant by Tolkien to be analagous to the real life conflicts that arose between the Anglo-Saxons in England and neighboring Celtic peoples.
This is supported by the fact that placenames of Bree-land like Bree, Archet and Combe are Celtic. The Stoor Hobbits (who had stayed long in Dunland), have Celtic elements in their names. Tolkien mentioned that the survival of traces of the older language of the Stoors and the Bree-men resembled the survival of Celtic elements in England.