For example, if the hand is:

Spades: A, 2
Hearts: K, J, T, 9, 2
Diamonds: 3
Clubs: K, Q, 7, 4, 3

Then this hand has 13 hcp and a distribution of 5-5-2-1 (the distribution is usually listed in non-increasing order). A balanced distribution is any one of 4-3-3-3, 4-4-3-2, and 5-3-3-2.