This summary is not the rule. The rule text controls.
Here's a plain-English summary of this rule:
The Alabama Supreme Court keeps an official list of every attorney who is allowed to practice before it. The court clerk is the person in charge of maintaining this list.
Attorneys get added to the list in the order they were admitted to practice, basically like a sign-up sheet that grows over time. This creates a permanent record showing who is licensed to appear before the court and when they were approved.
For most people involved in a case, this rule works quietly in the background. It does not directly affect how your case is handled, but it explains how the court keeps track of which attorneys are officially recognized to practice law at that level.