Subjects are terms in the record that describe the content of a piece of information. These terms come from a restricted list so you don't need to come up with synonyms when searching. Using subjects will retrieve fewer results, but they are potentially more relevant.
Keywords are any words that may appear in the record for the resource or in the full text. They retrieve many results, some of which will be irrelevant. They are best used for words that wouldn't be used as subjects, like jargon or proper names, or for when a variety of words best describes the topic.
Look for subject terms in a tab called "Subjects" or "Thesaurus" depending on the database. To apply the subject to your search, type the subject in the box on the advanced search screen and choose "Subject" from the drop down menu.