It is extremely important to understand that "One Time Pad" is an element of the actual cipher used, not any particular protocol. For example, SSL or TLS using RC4 is, effectively, implementing a digital One Time Pad, while SSL or TLS using DES or AES is not using one.
One Time Pad refers to the old-school cryptographic technique of printing code pads... actual paper things... that could be used to encrypt and decrypt messages. The pad was effectively the key to be used to encrypt a message.
The strength of a One Time Pad derives from the fact that your messages are generally short and the key is used one and only one time. This makes statistical attacks against the cipher text difficult. However, should you reuse the key, you instantly begin to compromise the overall security of the data, making a statistical cryptanalysis more viable.
There are other important features, however. Since a One Time Pad uses the key only one time, it also means that you get Perfect Forward Secrecy for free. PFS means that should an attacker "break" a key, either through a chosen plaintext, a known plaintext or other cryptanalysis, breaking that key gives you absolutely no information about any previous key or any future key, except, of course, that those keys are not the current key.
In practice, digital one time pads do not change the key after every single message. If they did, that would be fantastic, but it's simply not practical. To offset this deficiency (key reuse) implementations typically include two things. The first is a protocol or method to periodically replace the fixed portion of the key based on time or the amount of data sent. The second is to use some type of random "initialization vector" (think of it as a big salt) that is added to the key before encrypting each message. Rather than changing the entire key, a fixed (typically a relatively large portion of the key) remains fixed for some period of time while the IV (salt) is changed with every message. Since the salt is changing, it must be communicated to the communication partner and is typically sent either in the clear or effectively in the clear.
A wonderful example of a digital one time pad is RC-4. An example of a poor implementation (well known, of course) is WEP, which uses a 24 bit initialization vector. WPA, the first attempt to "fix" this, made the fixed portion of the key larger and added TKIP to periodically change to a random key (fixed portion) while still using RC-4 and IVs.