As the title says, I received an email yesterday, presumably I am in Cc of the email that my professor wrote to the university I am applying to. In my understanding there is always some mystery about the letters. But what exactly is the norm here? Does anyone care?
It is becoming more widely accepted that people have the right to be aware which information is kept on them by various organisations, to request access to this information and in some cases to request this information to be deleted (see e.g. FOI for UK, GDPR for EU). So by cc'ing you in, you professor acknowledged your right to access the same information about yourself that (s)he is sharing with the third party.
No, it does not reduce your chances — it is perfectly reasonable for professor to show the recommendation letter to the candidate, if they wanted to, and in some places it is even required.
Your comment clarifies that you were blind-copied (BCCed), not open-copied (CCed). That means that the college you are applying to would have just received a regular letter-of-recommendation with no apparent CC in the list of recipients (i.e., the do not know that this professor copied you into the message). As to whether this is normal, there is no standard here; it is a matter of discretion. Professors sometimes give a private letter-of-recommendation without disclosing to the student what they wrote, and sometimes they copy the student into the letter, so he/she can see what they wrote. When copying the student into the letter, some professors do this via blind-copy, so that the college does not make a negative inference about the candour of the letter.
I would say NO, it does not reduce your chances. Why would you think it would? A letter of recommendation is no secret. Even though it seems from the comments you were in BCC (so nobody can know).
Maybe think about it this way: You have certain qualities or capabilities. You professor obviously thinks that these qualify you for what ever he is recommending you. So there are no secrets anyway. You and your professor knew your capabilities and now the receiving party knows as well. It should not be a surprise to anyone, that you know why you are recommended.