Enabling alternate names gives you a place to enter an "Alternate" name for people and some other things as well. A common use for an alternate name is as the name in a different language. You can edit a person's other (non-primary) names by clicking on the Other names link in the Profile editor. The alternate and phonetic names are also available in mail merges, most custom reports, and in exports.
The fields "He" (males), "She" (females) and "They" (unknown gender) affect how the fields He/She/They and he/she/they (lower case) work when reporting on people or using them in mail merges. These are particularly useful in mail merges when you are referencing the person, e.g. "He has performed 145 hours of service in the past year." By placing the field He/She/They in the letter template, VSys will automatically use the appropriate pronoun.