This surname, has a number of derivations:

1.  English: someone who lived on or by a moor.

2.  English: someone who had a swarthy complexion [i.e. "like a Moor", itself derived, via French, from a Phoenician word meaning "from the east"].

3.  English: from various early saints' forenames, also from the same source as #2.  This gave rise to the use as a given name, introduced into Britain by the Normans, but is rare in English.

4.  Irish: an Anglicised form of the Gaelic "Ó Mórdha" = "descendant of Mórdha", Mórdha meaning "great, proud, stately".

5.  Scottish & Welsh: A nickname for a large man, from 'mór' in Gaelic, 'mawr' in Welsh.