In each exercise, you are asked to identify between one of two possible chord types.
Major and minor chords have pretty distinct sounds from one another, and yet there is only one half-step of difference between the two chords (major third versus minor third). Major chords tend to send "happier" than minor chords, which are generally associated with a "sad" sound. Play a few on your own to get a feel for the difference in sound, and then work on these exercises.
Major and augmented triads both share the major third interval, but the augmented triad has an augmented fifth on the top instead of a perfect fifth (from the root). Augmented triads are also very distinct from other chord sounds and should be relatively easy to identify once you've played and listened to a few.
Minor and diminished triads are also closely related, but the diminished triad has a diminished fifth on top instead of a perfect fifth. If minor chords are "sad," then diminished chords could be described as "sadder." Diminished chords also always sound like they are leading somewhere - you will never have the feeling that the diminished chord is final or completes a resolution. Minor chords, by contrast, can be used as passing chords but can also stand as a final chord in a progression. The tritone interval present in a diminished triad is also very distinct from the much more consonant perfect fifth interval in a minor triad, so if you practice listening to intervals, the presence of a tritone (or lack of one) should be an immediate tip-off.
The notes presented in the worksheet are the roots of each chord. As you listen, write down the quality of the chord (major, minor, etc.) and then later go back for some extra theory practice by filling out the missing notes of the chord in the staff. Every chord should be a series of stacked thirds with the appropriate accidentals. (One exception is with augmented triads, which are often messy to spell correctly with stacked thirds - occasionally I respell one note in an augmented chord to avoid double sharps and flats.)
Exercises 1-6 deal with major and minor triads. Exercises 7-12 deal with major and augmented triads. Exercises 13-18 deal with minor and diminished triads.