The Dorian mode is the second mode of the major scale. For example, C major is C D E F G A B C, or 1 2 3 4 5 6 7 1. Starting on the second note gives D E F G A B C D, or 1 2 b3 4 5 6 b7 1. We call it D Dorian when we start on the second note of the C major scale and play from D to D.
Another example: Bb major is Bb C D Eb F G A Bb (1 2 3 4 5 6 7 1). Starting on the second note gives C Dorian: C D Eb F G A Bb C (1 2 b3 4 5 6 b7 1).