A unit is usually 1% of your gambling bankroll. This is why it's usually a constant. If your gambling bankroll is $1000 and you win 100 units ($1000) usually your gambling bankroll would still be $1000 and the rest would just be profit. In Vaughany's case if he has stated that a unit is $10 he would probably be up $3630 according to his units. You can always change your bankroll, but most handicappers keep it about the same. This makes it a lot easier to keep track.
If you were to follow someone's pick you would be best off seeing what there unit sizes are and make adjustments to what works for you based on your bankroll. Just adjust your units to what you are comfortable and keep them constant until you want to increase or decrease your bankroll. Units make things very easy because they allow people to bet based on their bankroll rather than betting based on someone else's.