The first offer is a skill s/he already has but which is not yet at expert level. If a hero does not already possess eight secondary skills, he/she gets an offer of two different skill during level-up.
Each hero can have up to eight secondary skills. Typically in custom scenarios heroes start with either two secondary skills at basic level or one at advanced level. Each level increases the capability of the secondary skill making it more influential. There are 28 different secondary skills and each one has three levels: basic, advanced and expert. Secondary skills are beneficial qualities of heroes.