Viking is an activity, not a race. :) Viking tattoos represent the culture of Northern European people (also commonly referred to as Norsemen, meaning north men) which were heavily involved in trade and travel. Though some were involved in mercenary work, pillaging, piracy, and raiding, they were by no means alone in these endeavors during this era since much of the world was developing and in chaos.
They were also a people of lore, mysticism, and poetry. Wonderful stories were handed down through the generations involving different Gods, Goddesses, creatures, and realms that both help, or hindered their existence, depending on the circumstances.
The Viking era occurred between the eighth and eleventh century AD, so approximately a few hundred years in a region that is far older (around 7500 BC) and has made many wonderful contributions since.