Alpha in software and game development terminology refers to a period of time where the software is in very early stages of development. Alpha is closed to most members of "the public" and is only used by people within the company developing the software. Sometimes small groups of people close to the company may be invited to participate in alpha. Alpha can be used to determine the flow of the software, how things will work, and implementing early "back-bone" features.
Second Life's alpha was a bit unusual in that people who were interested in helping to develop the world could sign up for a program called "Early Creators". The early creators were in large part not only testing how SL would work, but also building the world so it did not seem empty for other residents when beta began. These early creators could be considered some of the first "content developers" for SL. During SL's alpha stages it was called Linden World.
Alpha is also short for a texture's alpha channel (also known as transparency or opacity).