Sak Yant — bamboo-stick tattooing applied by monks or ritual masters — is a genuine spiritual practice in Thailand, not simply a tattoo style, and one visitors will see referenced (and sometimes offered commercially) around the island.
What it traditionally involves
Geometric and animal designs believed to confer specific protections or blessings, hand-applied using a long sharpened bamboo or metal rod, traditionally performed by a monk or ajarn (lay master) as part of a ritual rather than a purely decorative studio visit.
The tourism version
Sak Yant has become widely available to tourists at studios across Thailand, including Phuket — worth knowing that a commercial tourist tattoo experience is a different thing from the traditional temple ritual, even when using the same needle technique and designs.
Etiquette if you're considering one
Certain designs are traditionally reserved for monks or considered inappropriate for casual tourist use — a reputable studio or master should be willing to explain a design's meaning and appropriateness before applying it, and it's reasonable to ask.