The custom fields can be changed from Admin > Custom Fields.
When adding a custom field you can specify if the field will be used for a contact, lead or both.
If lead or contact_lead is selected then the field will be displayed under the new lead window.
If a field is marked contact_lead, the value of the field will be transferred to the client side as well upon conversion of the lead.
If a field is marked as private then it will only be displayed in the details window after you click on the lead. If the private checkbox is unticked then the field will be displayed as part of the leads table.