Campaign member records are the link between your People (or Organisation) and your Campaigns. It allows you to store and track information about that particular person that is only relevant to that campaign, rather than storing an ever expanding list of temporary or changing information on the person themselves.
In plain English; a campaign member is the record of someone you'd like to target with a campaign, or that has been involved in a campaign.
Campaign member records are deliberately quite simple, but what might you store on or track with the Campaign member record?
A status dropdown field - A person may have been 'Contacted', or maybe your request for volunteering or fundraising was 'Successful'.
A notes field - Feedback on the contact you had with them or information for follow up messaging.
Using filters, you'd be able to view or export lists of people associated with a campaign to call, visit in person, send promotional material, etc.
Use a pipeline view to track and change the status of each campaign member, making it easy to see what stage each member is at.
See the full guide about campaigns for more details.