Multiple database collections are a group of databases under one umbrella. Usually they are searchable all at once. You can choose to search all of the databases (not very efficient), or select those that seem most appropriate for your subject and search them all together (a much better choice).
For instance in EBSCO, for a setting up business search, you can select the default databases (they are multidisciplinary, so cover a lot of subjects), the two business databases and the Religion and Philosophy database (for ethics). You can search all six databases at once using your key words with 'and' between. This technique can be used with most multi-database collections.
Databases that are not part of a collection must be searched individually. Read the database description and determine if it is appropriate. Use the key word with 'and' technique to search each database