So for the purpose of this example let's assume there is a king.
The king has two sons.
The eldest is going to inherit the throne, it is well known and acknowledged.
The eldest has his own son.
The eldest son dies before the king does.
Does the throne then ignore the grandson and default to the younger brother, or does the "line" continue?
Under primogeniture, succession follows a 'depth-first search' approach (descendants of elder siblings take precedence over younger siblings).
This means, in your example, the grandson inherits.
If the grandson was to die before the king, then the king's second son would inherit.
Another way of looking at it is that the inheritance passes to the oldest line until it dies out. If a king has two sons the line could be considered split into two - the oldest of which will always inherit unless no one is left who is eligible.
Eg:
The king has two sons named '1' and '2'.
1 has two sons named 1^1 and 1^2
2 has two sons named 2^1 and 2^2
The line of succession is: 1, 1^1, 1^2, 2, 2^1, 2^2
You can keep adding to this too. For example, Louis XIV was succeeded by his great grandson who was, using the above notation, 1^1^2.