This is a pretty old clip, but it shows in essence what an eye tracker does. As a researcher I need to analyze how my participants process visual information when they look at images I present to them. With eye tracking I can detect where the gaze goes, how often it goes there and for how long the gaze lasts. Since my hypotheses are that oxytocin will lead my participants to be more prone to illusory face perception, to rate non-facial faces more face-like, enhance eye gaze to facial stimuli, will lead participants to gaze longer and more frequently toward the eye region of facial stimuli, and respond faster to illusory faces – compared to participants assigned to receive placebo, the eye tracker will give me output which will (hopefully) confirm my hypotheses.
Eye tracker might also improve the effectiveness and verifiability of my study by filtering out trials where the subjects failed to see the stimulus, or to comply with the task. Compared to fMRI or EEG, there is less statistical noise, leading to fewer subjects needed and thus faster results, which most likely improve the efficiency of many studies.
I can also measure the pupil dilation/contraction, which will give me some input regarding emotional states or task difficulty.