A PKCS#12 file can contain both the certificate and the private key. They are, however, stored as separate, distinct objects. The certificate itself has the public key embedded within it. Since the certificate only contains the public key, it is considered "public" as well. You can feel free to distribute the certificate, as it does not contain the private key, which should be kept confidential. This is the basis of the security in asymmetric cryptography.
Because a PKCS#12 file contains both items, it is encrypted with a password to protect the private key within it. That said, you would use the private key to prove that the certificate you distribute belongs to you. For example, through the use of a digital signature on a document.
Hope that helps!