There are many possible ways. Priyan's method is essential but many other ways could be made up. Depending on your data quickness of computations may play important role.

data = RandomReal[4, {10^7, 2}];

method1 = Cases[data, x_ /; 1 < x[[2]] < 2]; // AbsoluteTiming
method2 = Select[data, 1 < #[[2]] < 2 &]; // AbsoluteTiming
method3 = Pick[data, IntervalMemberQ[Interval[{1, 2}], data[[All, 2]]]]; // AbsoluteTiming

{21.470108, Null}

{17.848240, Null}

{27.011183, Null}

method1 == method2 == method3

True

Generally your questions is basic and deserves first of all checking Documentation.