AP and DP brackets are set ranges that give bonus AP or extra damage reduction. For example, once you hit 100 AP, you get an extra base 5 AP. Only your “sheet AP” and “sheet DP”, which is the AP/DP shown in your equipment window, counts towards the AP/DP brackets (all hidden AP/DP will not count).
You can view the bonuses from the AP/DP Brackets at any time by going to your equipment window (I) then hovering over the (?) next to your AP or DP.
It is also worth mentioning that the AP brackets are seperate for your mainhand and awakening. So if you have 260 mainhand AP, and 261 awakening AP, then you will have an extra 83 AP on your mainhand and extra 101 on your awakening AP.
You should always consider and reference AP and DP brackets when upgrading your gear. For example if you are 260 AP, you may want to put a caphras level into your weapon to bring it to the next bracket. It may look like you are spending a lot of silver just for 1 AP, but you would really be gaining almost 20 AP if you consider the extra bonuses that AP brackets provide.
Kutum vs Nouver
There has always been a debate as to whether Kutum or Nouver is better for your class. If we consider the offhands on their own, kutum is better for PVE due to the extra monster damage, and nouver is usually considered better for PVP because of the higher AP.
However, when you consider the AP brackets, this can change. Once you are over 261 AP whilst using a TET Nouver, the extra damage from the AP bracket pushes the damage of a nouver to higher than it would be using a TET Kutum in PVE. It is only once you are over 265 AP whilst using a TET Kutum, where it is better to use the Kutum again. During this gap, players often sell their TET Kutum to help work towards other upgrades, and then buy it back again at a later date.
There are other situations where this happens and here you can find a full table with a calculator to help you work out which is best for you and your current gear.
AP Bracket Table
DP Bracket Table