The permit of residence (in French “permis de séjour”) is your identity in Switzerland. It is recognized by the whole Switzerland and it’s necessary whenever you have to deal with the authorities. In addition, it’s necessary for most Swiss Banks in order to open a bank account and have a credit card. Usually, after you apply for the permit, you need to wait between 2 weeks and 3 months until you receive it.
Until you receive your permit, you need to use the residence certificate (attestation de residence), which you’ll receive the day you submit the application for the permit.
For more information regarding residence permit, you can check the dedicated page from the service of Student Affaires (SAE).