MeSH makes sure that every new and old medical term is referred to in one single, controlled way, so if you're looking for publications related to a term, you know you're getting the most accurate results.
When you search in PubMed, you are using MeSH terms whether you know it or not. Find your search history in the Advanced section, and there you will find PubMed's internal workings based on your search strings. You can also use the Advanced Search Builder to incorporate MeSH terms into your search string directly.
Or start at the beginning with the MeSH browser to choose the ones you must use in your search string for the fullest results.