The tack is the force required to split a thin fluid film of the printing ink between the paper and the printing surface, touching only momentarily, therefore indicative of the ink's internal cohesion.
The tack value of an ink gives a guide to an ink film's resistance to splitting at impession (printing).
The grreater the tack, the greater the stress put on the paper.

Here are also a couple explanations from the web;

Tack
The tack of an ink is the force required to split a thin film of ink as it transfers down or up the ink train from roller to roller; roller to the plate; plate to the blanket; and blanket to the stock. The ink formulator will use an instrument called an Inkometer to measure the tack and will use this instrument to help him adjust the final formulation of the ink. The measure ink tack and the stability of ink tack an Inkometer is used.
www.dynodan.com/printing-process-explained/lithography-file...
“Ink tack” can be defined as the “stickiness of an ink” similar to what you would feel if you try to pull your fingers apart with ink between them.
pffc-online.com/mag/paper_role_tack_printing/