It means 'phantom' (lit. "magical art"); cf. the Old English word gedwimer 'sorcery'.
It is not clear whether the word refers to a creature of the Rohanese folklore (like the holbytlan) therefore when Eowyn confronted the Witch-King she rather identified him with one, than coining the word on that moment. There is some possibility that Dwimmerlaik is how the Rohirrim called the rumors of the Nazgûl in general.
David Day in A Tolkien Bestiary considered that a Dwimmerlaik is any creature of Rohanese superstitious folklore that includes Elves and Ents. However there is no indication in Tolkien's writings that the word pre-existed or that it was used for other races.