Ranks are a cosmetic game mechanic in Critical Strike Portable and Critical Ops. Ranks are a way to indicate a player's status, although this is represented differently between both Critical Strike Portable and Critical Ops.
In Critical Strike Portable, they are determined by the player's kill/death ratio and in Critical Ops, they are determined by how many total ranked games a player wins or loses.
These have no real gameplay advantages or disadvantages whatsoever, other than for cosmetic use.
Ranks are earned through playing ranked games, which are accessible through the main menu. In order for a player to rank up, they must win 10 placement matches, which consist of 9 total rounds won (unlike casual which consists of 13). The opposite can also occur, so if a player happens to lose enough rounds, they will rank down.
Critical Strike Portable
Ranks label a player's kill to death ratio, and gives a general idea on their skill. The higher the kill count than the death count the lower the rank. Higher ranks are determined by lower numbers, so for example, the highest rank a player can attain is 1, and the lowest (and initial) rank is 64.
In order to rank up, a player must improve his/her kill/death ratio by killing players more often than dying. Dying more than killing will cause the player to rank down.