First, we all develop auditory awareness. We simply become aware that there are sounds around us. You will notice that small children will begin to localize to the sounds. Localizing is when you turn your attention (and usually your face) toward the sound in order to see what is making the noise.
Second, you begin to develop auditory discrimination. You are already aware of the sounds and now you begin to determine what makes each sound and the differences in sounds. You do this for both environmental and speech sounds. What kind of discriminations do you make with speech sounds? Well, you can begin to tell a difference in the stress of the words, duration of sounds, rate of speech, pitch of the sounds, intensity, volume, and the voice/place/manner of the sounds.
Third, you will begin to develop auditory identification. This is even more sophisticated than simply discriminating. Now you are adding meaning to the sounds that you hear. You begin understanding auditory association. That means that you will know that when you hear a doorbell, that means that someone is at the door and you should go check. You also begin to develop self-monitoring skills. If you say something wrong, then you correct yourself. This is also the time that kids begin to develop phonological and phonemic awareness skills (approximately 4 years of age).
Lastly, you develop auditory comprehension skills. This is what you hear, understand, and respond to correctly. These skills include being able to fill in the blanks, following verbal instructions, answering questions about something heard, remembering things you have heard (auditory memory), and auditory processing skills.
I hope these descriptions were general enough in nature that you can kind of see where your child falls in his/her auditory development.