I am not an Ukrainian native speaker, but according to Ukrainian-Czech it means someone who is driving a car (also a taxi).
Does й usually have a sound? I usually see it at the end of words and it sounds like it is not really pronounced?
Yes, it does have a sound. For example, it is clearly pronounced here. The sound is "y" is "yes", and it is also used to make diphthongs ай, ий, ій, ой, уй, ей. Still, it is usually considered a consonant in Ukrainian and Russian because there aren't many diphthongs there and these do not add anything special (not to mention, they are not perceived as a single sound by native speakers).
English has [ɔɪ] as in "boy" but does not recognize anything with two "i"-like sounds. That's why it might be hard to hear for you. What might add to the fire is the slight diphthongization of normal vowels ("me") in some speakers.
To get a better understanding of what you should listen to, try pronouncing it yourself first. Start with the vowel from "tea" and then close up to the consonant in "you" (which is a tenser sound). In natural speech these endings do not normally have Й that exaggerated but you'll get the idea.