This issue can affect RSA computations in crypto/rsa, which is used by crypto/tls. TLS servers on 32-bit systems could plausibly leak their RSA private key due to this issue. Other protocol implementations that create many RSA signatures could also be impacted in the same way.
Specifically, incorrect results in one part of the RSA Chinese Remainder computation can cause the result to be incorrect in such a way that it leaks one of the primes. While RSA blinding should prevent an attacker from crafting specific inputs that trigger the bug, on 32-bit systems the bug can be expected to occur at random around one in 2^26 times. Thus collecting around 64 million signatures (of known data) from an affected server should be enough to extract the private key used.
On 64-bit systems, the frequency of the bug is so low (less than one in 2^50) that it would be very difficult to exploit. Nonetheless, everyone is strongly encouraged to upgrade.