Tier
Tier is a term used for several different types of item or effect, to distinguish more powerful versions of the same thing.
For all uses of tier, a higher number means a more powerful or higher level item. Note this is different to Path of Exile 1, where Item Affixes and Unique Rarity tiers worked in reverse.
Waystones
The tier of a waystone determines the area level of a map created with that waystone, with each tier being one level higher than the previous one. Waystone tiers can be seen on the item icon in roman numerals.
Item affixes
Explicit modifiers on items have a tier, which is in comparison to other modifiers in the same group, i.e. which do the same thing. These tiers can be seen when you hold Alt when hovering over an item.
For example, a tier 1 increased life prefix might give an item +10-19 maximum life, a tier 2 +20-29, and so on. The number of tiers depends on the specific type of modifier - for some modifier groups tier 2 might be the highest possible, while others go much higher.
Unidentified rare items
In Endgame, some rare items will drop with a tier appended to their name. This affects what mods can roll on the item, with a higher tier rare more likely to have higher tier modifiers. This only affects the mods revealed by identifying, it does not affect any future crafting.
Uncut gems
The word Tier is sometimes used by players for the gem level of an uncut gem, or of different levels of support gems, to distinguish it from character levels. However, the game always uses "level" to describe gem level. Like waystones, uncut gems display their level in roman numerals.