What do do unions want politically?

Power.  Most unions have a communist bent.  Look at their policies and
practices.    Take for example the teacher's union in NY City.  It
takes years and thousands of hours of effort to fire a teacher.  While
I don't think people should be fired willy nilly, taking years and
thousands of hours of resources to fire an incompetent teacher or a
teacher who sexually harasses a student is too far on the other end of
the spectreum.  Yes, there is currently a case of a teacher repeatedly
sending highly explicit emails etc. to a female student and under
union rules it is going to take years to fire the teacher.  The
problem is so bad that NY public school system has a couple of
buildings where they house teachers to keep them away from students. 
They pay the teachers to show up to an empty room and pay tens of
millions of dollars a year so they don't divert reseources to try to
fire them.  It is sickening.  That is what unions are for.

Unions would have never come about being if companys were fair to
there labor force! Many employers do not treat their labor fairly and
equally so unions started to form.
   Companies spend BILLIONS of dollars annually to lobby politicians
so they can get laws passed in their favor. So unions have had to get
politically involved to try to prevent this from happening.
   So to answer your question. They want laws in effect and enforced
that help to protect the people who work and allow them to make a fair
wage, have medical , dental, vision, and prescription coverage. As
well safe and good working conditions.
   Unions are a good thing for the working class! union workers make
25% to 40% more in wages and benefits.

american unions are usually most concerned with the welfare of their
own members.  things like better working conditions, pay and benefits,
and job security.  they also want to acquire more dues paying members.
 a shop union that is contained to one business, will aspire to become
an industrial trades union like the UAW which represents employees of
all 3 US car manufacturers, or the IFCW which represents thousands of
different local unions in supermarkets.

but most western democracies, especially europe, take it one step
further.  there the labour movement often represents a strong
political force.  the ultimate objective is to organize as many
unions, as well as churches, charities, environmentalists, student
groups and other non-governmental organizations into a powerful
political force and political parties.  here the objective would be to
press for policies for working people.  things like a national labour
law that is generous to workers, regulations against outsourcing of
jobs, economic policies to maintain full employment (employers hate
that), even demanding for more protection of the environment