The Celtic cross typically refers to any variation on a cross design done in the style of a Celtic tattoo. More specifically it may refer to "Odin's Cross" (the symbol on the left) which was the symbol for the Celts of Ireland and Scotland. In more recent times the symbol has been co-opted as a "white power" or "white pride" symbol, being chosen as a logo by groups such as Stormfront and Skrewdriver.
That said, unlike the swastika, there is still a great deal of culturally accurate positive usage of this symbol in the West (it is also a Christian symbol), so one should not automatically assume that the person wearing it is a racist.
A few other implementations of Celtic crosses are shown below — the variations are almost endless, and while they are normally tattooed in place, they can also be scarred in place (as shown in the third photo).