Why does my MA return only say started? My federal return has been accepted already. Thanks

The Massachusetts state forms are not yet finalized and available for filing until another few days.  It looks like most MA forms are projected to be available sometime on 1/26/2018.    See the dates in this table:

State forms availability dates:
https://ttlc.intuit.com/questions/1908857-state-forms-availability-table-for-turbotax-individual-per...

Once the MA forms are final and when it says "available" in that table, you should be able to go back and efile the state return.

You said your Federal return has been accepted.   That's early.  You must have had one of the few Federal returns the IRS pulled early for testing purposes.   They won't officially start processing season until January 29.