In simple terms you can say that basking is to enjoy the pleasant warmth of something. But figuratively the word has several uses.
One of the most common uses of the term is to enjoy the success of somebody who is quite close to you and not feeling jealous of his or her success. Suppose you have a wife who is winning a lot of accolades for her performance and you are not faring as well as her. In most of the cases the husband felt jealous of her success and want her to be under himself. But there are some magnanimous people who just love the success of her spouse and for those people you can say that they are basking in their wife's reflected glory.
One of the most common uses of the term is to enjoy the success of somebody who is quite close to you and not feeling jealous of his or her success. Suppose you have a wife who is winning a lot of accolades for her performance and you are not faring as well as her. In most of the cases the husband felt jealous of her success and want her to be under himself. But there are some magnanimous people who just love the success of her spouse and for those people you can say that they are basking in their wife's reflected glory.