LAuth is a protocol to authenticate HTTP requests.
There are three actors in LAuth. A CLIENT needs to have access to a USER's resources on a SERVER.
The goal of LAuth is to enable servers to verify the identity of a client acting on behalf of a user without the user having to give to the client the secret he shares with the server.
What does this mean?
For example, let's say Alice have uploaded photos on photos.example.com, using a login name and a password that give her access to the whole range of services offered by photos.example.com.
Alice also have a Drupal site, drupal.example.com, on which she installed the ExampleAlbum module. Using ExampleAlbum, Alice can display the photos she uploaded on her account on photos.example.com. ExampleAlbum thus needs access to Alice's account on photos.example.com. However, for security reasons, Alice does not want to give her photos.example.com credentials to ExampleAlbum module.
Fortunately, ExampleAlbum and photos.example.com both support LAuth.
So Alice logs on photos.example.com and generates a new LAuth key. She then copies the key (a key identifier and a secret) on the configuration page of the ExampleAlbum module. The ExampleAlbum module will use this key to make signed requests to photos.example.com on behalf of Alice.