Narrative present refers to the use of tense in one's writing. It is the way the time of the narrative is arranged and presented to the readers. When the time is referred to as something that is happening in the present, then it follows the pattern of the narrative present. It is used to create a sense of immediacy in one's writing.
Narrative present uses simple present. Simple present is used when a narrative is based on something that is happening right at the moment or when it happens regularly. It always has 's' or 'es' added at the end.
  1. I sing well
  2. She dances well
  3. She walks towards her home
  4. The bear looks at him
A narrative present uses simple present tense to give the effect of something happening at the exact moment the reader is reading. It helps the reader be engrossed and makes it interesting. It also helps the reader feel that he is part of the work. This is also a reason as to why sports commentary is always in the simple present.
The lesson "A Bond of Love", has certain paragraphs completely in the narrative present, especially when something of immediate need or urgency is narrated.
A dash back to the car. Bruno still floundering about on his stumps, but clearly weakening rapidly; some vomiting, heavy breathing, with heaving flanks and gaping mouth.
Hold him, everybody! In goes the hypodermic—Bruno squeals — 10 c.c. of the antidote enters his system without a drop being wasted. Ten minutes later: condition unchanged! Another 10 c.c injected! Ten minutes later: breathing less stertorous — Bruno can move his arms and legs a little although he cannot stand yet. Thirty minutes later: Bruno gets up and has a great feed! He looks at us disdainfully, as much as to say, ‘What’s barium carbonate to a big black bear like me?’ Bruno is still eating.
In this paragraph, the bear is in great danger and the author explains the events as though he is giving a live commentary, to emphasize the importance of the situation. The short sentences and the simple present (words like squeals, enters, gets etc.) together creates an effect in the reader's mind, as though they are a part of the story.