Tier in Torment: Tides of Numenera measures the strength of your Character.
The XP system in Torment: Tides of Numenera is very different from Torment: Planescape (and many other RPGs). Instead of level, Tides of Numenera use Tier to represent your character's strength. Each tier is divided into four steps, once your character gathered enough XP, he or she can take an advancement in steps. Each step characters can chose to increase their max Effort, Stat Pool or Stat Edge. Alternatively, they can pick new skills or abilities (or enhance old ones).
Once all four steps is complete, character advances to next Tier. Then, as you gain XP you can continue to gain benefits (as well as new tier abilities)