Mapping custom fields is used to map fields information and values so that information is maintained during the lead conversion process. When a lead is converted to an account, contact, and opportunity, the lead record will no longer exist. Standard fields are automatically mapped by the application, but custom fields will need to be built with mapping to make sure you maintain information.
To maintain information during conversion, you must create the same field from the leads module in the module that should retain the information. For example, if I'd like to track which product my lead is interested in, I might want that to be maintained on the opportunity upon conversion. To maintain the information, I would create a field with the same values in the Opportunity module and map the field. Mapping can be completed by selecting the ‘Custom Field Mapping Button’ on the 'Leads' section of the custom field editor.