'Loose ends' are pieces of thread that are visible after sewing something. When you 'tie up loose ends' it means to finish or complete small things that are the result of a previous action or which have been incompleted. This is an idiomatic expression used in both professional and social contexts. Similar in meaning to '
dot the Is and cross the Ts', or 'bring to a close'. If you 'leave no loose ends' it means to avoid leaving any small tasks unfinished. If you say 'there are still a few loose ends' you mean there are a few things left to address or to deal with.