I also agree with Stefan, it’s a reminder, not just for Harry - but Dumbledore feels that it should be a reminder and a warning to all wizards who see that scar (or know about the scar).
Dumbledore is worried that memories of Voldemort and the terror he inspired, will become diluted, people will start believing (over time) that it is impossible for Voldemort to come back.
Dumbledore knows Voldemort will return somehow.
from Deathly Hollows chapter: The Prince’s Tale
while Harry was examining Snape’s memories in the Pensieve. This was the memory of events right after Lily’s death
“You know how and why she died. Make sure it was not in vain.
Help me protect Lily’s son.”
“He does not need protection. The Dark Lord has gone —”
“The Dark Lord will return, and Harry Potter will be in terrible
danger when he does.”
Imagine going back to the time of Lily’s sacrifice
a few days after the news hits the newspapers, a good number of wizards might be 50 percent sure (in their mind) that Voldemort is dead.
a month later maybe 54 percent sure (in their mind) that Voldemort is dead
1 year later maybe 70 percent sure (in their mind) that Voldemort is dead
until many years later when uncertainty slides into certainty and many people think - 100 percent sure (in their mind) (that Voldemort is dead).
Goblet of Fire chapter Parting of ways
“See here, Dumbledore,” said Fudge, and Harry was astonished
to see a slight smile dawning on his face, “you — you can’t seriously believe that. You-Know-Who — back? Come now, come
now . . . certainly, Crouch may have believed himself to be acting
upon You-Know-Who’s orders — but to take the word of a lunatic
like that, Dumbledore . . .”
Fudge would have reacted differently if Voldemort came back a month after Lily’s death.
“don’t let your guard down” was Dumbledore’s message.
Dumbledore was hoping wizards will remember the fear and uncertainty they felt during the first days of Voldemort’s “supposed” death (if they see the scar or talk about Harry and his famous scar).
Of course wizards generally do not like to dwell on fear and uncertainty.