Introduction to Twelve Monkeys from the Programme Notes:
And, his stark look was further enhanced by his makeup artist, Cristina Bartolucci, who, everyday, etched a trio of tattoos onto Willis' scalp and neck - one that indicated his prisoner number, and a pair of bar-codes, the kind imprinted on packaged goods, on each side of his neck.
This is also repeated on Wikipedia:
The actor had a trio of tattoos drawn onto his scalp and neck each day when filming: one that indicated his prisoner number, and a pair of barcodes on each side of his neck.
I don't think that there's any particular significance to the tattoos other than to emphasise the dystopian undercurrent in the story and remind us every now and then that Cole is actually a prisoner (from the future).