To act generously means to give or share freely and abundantly, like happily sharing half your lunch with a friend who forgot his.
When people act generously, they give more than what's expected or required, often motivated by kindness. For example, someone who volunteers their free time at a local animal shelter is acting generously because they're offering their time without needing to — and without expecting anything in return. By acting generously, you help make the world a friendlier and more caring place.