memcmp compares two blocks of memory byte-by-byte. If the first two bytes don't match, the function can return early, otherwise it has to check the next byte. By measuring the execution times for all 256 possible bytes, one should be able to guess the first byte. Repeat this for the length of the memory being compared, and you should be able to essentially read the entire block of memory you're being compared against.
These attacks are usually done over a fast connection (maybe buy a machine in the same datacenter as your target), and through lots of measurements averaged together and measured for statistical significance.
We don't know where this function is used, so this might actually be a non-issue. We need someone more familiar with OpenSSL to comment.