The death of MD5 (and some SSL certificates)
Message Digest algorithm 5 (MD5 for short) is a one-way cryptographic hashing function. Put in its simplest terms, it takes input, mangles it, and generates a 128-bit value (usually expressed as a 32-character hexadecimal number such as 76ffd163bd23504cfeb873a9c027b2ed). The same input (e.g., password) will always have the same output (for example, 5f4dcc3b5aa765d61d8327deb882cf99). So why use MD5? When cryptographically signing data (such as email or SSL certificates), it is much more efficient to sign a cryptographic signature of the data rather than the entire block of data itself (128 bits of data compared with a kilobyte or more for an SSL certificate).
MD5 is widely used. For example, many Linux distributions use it by default to hash password values in the /etc/shadow password file, numerous SSL certificate authorities support it, and many application vendors use it rather than stronger algorithms such as SHA-1 or SHA-256 (a hashing algorithm similar in functionality to MD5).
The Trade-off
Like any security issue, a continuum of choices generally ranges from a combination of "cheap, easy, insecure, and computationally inexpensive" to "expensive, difficult, secure, and computationally expensive." In the case of MD5, it falls somewhere in the middle, not so much because of any conscious choices to cut corners, but largely because of its age (it was invented in 1991).
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