A phantasia character's abilities are determined by his/her statictics. These attributes change as a player ages or goes up in levels and can be enhanced with equipment found as treasure or bought at trading posts.
Here's a list of Phantasia's basic character statistics.
quickness - a higher quickness gives you better chance of winning initiative in combat. Quickness can drop when too much gold is carried or when the character gets tired from too much fighting without rest.
level - a general rating of a character. Each time a character goes up a level, most other stats are improved.
age of player - roughly equivalent to number of turns. As age increases, many personal statistics degenerate.