The official defintion of term is "a word or phrase used to describe a thing or to express a concept, especially in a particular kind of language or branch of study." In this case it's refrencing "downsizing", they could have said "...some people have started apply the term downsizing to their own situations". Term is similar to word or expression, so they're saying people are using that word/expression/term (i.e. downsizing), to describe their own situations.