What does "Our way is the old way" mean?

Observe the context and the underlying story:

• Bran is witnessing an execution.
• Ned is executing a man who has deserted the Night's Watch.
• The Night's Watch is a group that has sworn to safeguard humans from White Walkers. Those who join the Night's Watch, swear an oath to do so for the rest of their lives. Desertion is punishable by death.
• The Night's Watch has existed for thousands of years.
• Though I don't think it has been explicitly said, it's fair to assume that punishing desertion by execution has been the rule for as long as the Night's Watch has existed. At the very least, no one has ever argued that it is a recent tradition.

Bran's first guess is that the execution takes place because it has been a tradition to execute deserters. It's a rule that has been applied for many centuries, and should remain in active use.

Knowing this, let me translate Bran's words in the script:

Ned -- You understand why I did it?
Bran - Jon said he was a deserter.
Ned -- But do you understand why I had to kill him?
Bran - We follow the rules that have been followed for a long time already?
Ned -- The man who passes the sentence should swing the sword.