Growth Rates are a set of hidden stats that appears in each game in the series. For each increasable character stat, such as Strength or Speed, there is usually a growth rate associated with it. For playable characters, growth rates are the percentage chance of a character gaining 1 point in a particular stat during a Level Up, with the Random Number Generator used to determine whether a stat increases or not. For example, a growth rate of 50% on average yields 1 stat up per 2 Level Ups.
In rare cases, growth rates may exceed 100%. In which case, 100% is subtracted off the growth rate and becomes a guaranteed +1 during a Level Up, with the remaining growth rate allowing for a chance of another +1. Since the maximum growth rate is 255% (due to the games' programming), the maximum stat increase during a Level Up is +3 (which is possible with Karel in Fire Emblem: The Binding Blade, as he has a HP growth of 210%).
Enemy characters use a different set of growth rates, known as Class growth rates. Enemies do not Level Up in the traditional sense, but instead they are auto-levelled at the beginning of each chapter (or, for reinforcements, when they first appear). This is why enemies usually have slightly random stats. Class growth rates are also used to determine Hard Mode bonuses.
Growth rates are usually hidden from the player, although some guidebooks may list them or provide growth rankings (such as A for growths of 100% to 80%). Usually growth rates are obtained by hacking the games.