The text command is defined by the amsmath package through a subordinate package amstext (which can also be used independently if desired). The main use of the command text is for words or phrases in a display. It is very similar to the / command mbox in its effects, but has a couple of advantages. If you want a word or phrase of text in a subscript, you can type |..._word or phrase|, which is slightly easier than the mbox equivalent: |..._ |word| |or| |phrase|. The other advantage is the more descriptive name.
f_{[x_{i-1},x_i]} \text{ is monotonic,}
\quad i = 1,\dots,c+1