On my e-ticket for my flight with Swiss booked through Travelup.com, I see this:
Does this mean I'm only allowed hang-luggage? Or can I take hand-luggage, and check in one piece of luggage?
Airlines tickets usually report the amount of allowed checked baggages. Hand luggages are usually taken for granted.
However, in this particular case, the Swissair website says:
So I guess (if you travel in economy class) you are allowed one 23 kg checked baggage plus a 8 kg hand luggage.
It means that you are allowed to check in one piece of luggage free of charge (as long as it isn't over the maximum allowed weight and size).
Carry-on luggage is separate. For most airlines you are allowed two pieces of carry on. One that will fit in the overhead compartment and another that will fit under the seat in front of you.