Czygan (modern standard spelling Cigány) means "Gypsy, Roma" in Hungarian. It was used both as a literal ethnic term, and as a more generic descriptive for someone who was like a Gypsy in some way, such as dark coloring or frequent travel.

In modern Hungary, there's a lot of politics involving accusations of discrimination and sensitivities about proper terminology for Gypsy/Roma people, and yes, calling someone a gypsy can be perceived as an insult, depending on context -- but it's a common surname (most often preserving the slightly archaic spelling Czigány), so the name can hardly be considered inherently offensive. It falls into the same category as Bastard, I think, except for being much more frequent as a family name.

Origin: a conflation of two names. The earlier source is likely an Old Turkic-origin personal name Sďq{.a}n, which developed from the expression sď{.a}n s{.a}{cv} meaning 'smooth haired'. In Hungarian, the initial sz- [s] became c- [ts], following a normal pattern of sound changes (affrication) (such as for example szirok > cirok 'sorghum'). The personal name Cigán ~ Cigány became a common family name, and its diminutive in -d is found as a placename (Cigánd).
The other origin is the name of the ethnic group, now called Roma, that settled in Hungary in greater numbers starting in the 15th century. The term cigány is of southern Slavic (Bulgarian) origin, transmitted via Romanian. Earlier use was metaphorical, based on a cigány-like inner or external characteristic (behavior, wandering, dress; darker skin, black hair, beard, etc.), but especially after the law requiring the use of surnames (1787), it was used as a family name with its literal meaning as well.