a cryptographic hash function with a 128-bit (16-byte) output, now deprecated
An MD5 checksum consists of 128 bits (16 bytes) which are often presented as 32 hexadecimal digits.
MD5's collision resistance is broken: it is possible to find two strings with the same MD5 checksum (there can be some additional requirements on the strings, for example a common prefix). For applications that only rely on other properties such as preimage resistance (the impossibility of finding a string given its MD5 checksum, except by brute force), the attacks are only theoretical.
Applications that require a cryptographic hash should use SHA-2 instead. SHA-2 produces a 256-bit (32-byte) checksum (there are other, less common sizes), not 128-bit, so applications with a fixed-size field must be updated. SHA-1 is also a viable alternative; although SHA-2 is meant to replace SHA-1, there are currently no practical vulnerabilities in SHA-1 that SHA-2 solves.