trigger NoteCopy on Note (after insert, after update) {
    // Notes attached to leads
    Note[] leadNotes = new Note[0];
    // Just notes for leads...
    for(Note record: Trigger.new) {
        if(record.ParentId != null && record.ParentId.getSObjectType() == Lead.SObjectType) {
            leadNotes.add(record);
        }
    }
    // No notes to process? We're done.
    if(leadNotes.isEmpty()) {
        return;
    }
    // Update Lead records with new notes.
    Map<Id, Lead> records = new Map<Id, Lead>();
    for(Note record: leadNotes) {
        records.put(record.ParentId, new Lead(Id=record.ParentId, Note__c=record.Body));
    }
    update records.values();
}