Map the Lead Description standard field to Description fields on other objects

1. Export all the data currently residing in the Lead Description field as well as the Object's Description field that you want to map to (ex. Contact Description). This can be done using reports or using Data Loader. 

2. Create a custom Long Area Text field for both Leads and the other object. You can use Description as the Label and name of the field. 

3. Mass Update all Lead and Contact records to move the values from the standard Description to the custom Description field. You can follow the steps on this document.

4. Remove the standard Description fields from the page layout for both objects and then replace them with the custom fields.

5. After the fields has been created and updated, you can then use the Map Lead Fields option: Setup | Customize | Leads | Fields and select the Map Lead Fields button.