Guys, it took me about 10 minutes of superficial research to find out about how these appeal work. See
"Appeals against Arbitral Awards by the CAS" by Dr. Stephan Netzle as published on page 19 here: https://www.tas-cas.org/fileadmin/user_upload/Bulletin202_2011.pdf Yeah, it's a little bit longer than one paragraph, but not much, bear with me.
The CAS is an arbitration panel. Parties submit voluntarily to such panel's jurisdiction. Once they have done so, the panel's awards are binding on them - unless they are violating some minimum requirements of the applicable state legal system (such as right to be heard, basic procedural matters, ordre public etc.), that is. In which case a party can appeal to a state court - in our case, against a CAS award to the Swiss Federal Tribunal. Swiss for the simple reason that the CAS is a Swiss arbitration panel. If it was in Moscow, Russian courts would have jurisdiction. Which is why people prefer to submit to Swiss arbitration (and constitute arbitration panels there) rather than arbitration in Russia. Or, e.g. for commercial matters, the ICC in Paris. You would want a working and independent judicial system to supervise arbitration.
On the initial question: So, CAS rulings are binding on the IAAF. If the Swiss Federal Tribunal sets aside the award, there is no more binding award (interestingly, the Swiss court is also entitled to set aside the award on a point of law rather than procedural matters, however only if there are new facts). As the IAAF has submitted to arbitration by CAS, and the CAS is supervised by the Swiss Federal Tribunal, the IAAF has indirectly submitted to the fact that the latter has influence on the case. That's it.
These appeals generally do not have suspensive effect. But the Swiss court can take precautionary measures in order to maintain the status quo or to provisionally secure interests which are at risk until it decides finally on the appeal.
I am a German native speaker (no, not Swiss but nearby). My apologies if the English legal terminology might not be exactly on the point.