In this context the word "padded" is used to express a slight inflation of numbers. The word is most commonly used in relation to clothing or items of furniture. Eg a padded jacket, a well padded chair , the cushion had a lot of padding "etc. Another term in this context could be "stuffing" and both "padding" and "stuffing" mean to add content , to "bolster" to add filling , or in the case you highlight, to falsify extra votes.
Hope that helps!