We have a few things going on here.
First we must look at the context of Harry receiving 60 points.
‘First – to Mr Ronald Weasley, for the best-played game of chess Hogwarts has seen in many years, I award Gryffindor house fifty points.’
‘Second – to Miss Hermione Granger ... for the use of cool logic in
the face of fire, I award Gryffindor house fifty points.’
‘Third – to Mr Harry Potter ...’ said Dumbledore. The room
went deadly quiet. ‘... for pure nerve and outstanding courage, I
award Gryffindor house sixty points.’
Now further context, everyone KNEW about Harry, Ron, and Hermione passing the challenges and stopping Quirrell, maybe not 100% of the events, such as Voldemort possessing Quirrell, but they knew about the challenges.
Percy could be heard telling the other Prefects, ‘My brother, you know! My youngest brother! Got past McGonagall’s giant chess set!’
So now in context, and compared to, Ron and Hermione, Harry receives an addition 10 points for being essentially physically assaulted by Lord Voldemort, and showing courage and bravery through it all, and almost dying(remember Harry's been in the hospital wing for a few days now).
So now their points make sense, so what did Neville do to receive points.
A slight correction to @Slytherincess's question, but Neville did not recieve points "for when Neville attempted to stop Harry, Ron, and Hermione from engaging Draco Malfoy in a duel earlier in the school year."
He received points when on the night that Harry and crew left to fight Quirrell he attempted to stop them.
‘I won’t let you do it,’ he said, hurrying to stand in front of the
portrait hole. ‘I’ll – I’ll fight you!’
‘Neville,’ Ron exploded, ‘get away from that hole and don’t be an
‘Don’t you call me an idiot!’ said Neville. ‘I don’t think you should
be breaking any more rules! And you were the one who told me to stand
up to people!’
‘Yes, but not to us,’ said Ron in exasperation. ‘Neville, you don’t
know what you’re doing.’
So now Neville bravely stood up to his friends, before mortal danger was happening, in which Harry and crew received their 50+ points. Everyone knew Neville was not actually a part of those events, so his 10 points are simply a footnote in Harry and crew's adventure and success.
Another possible way to look at it is that Harry and crew were all a part of the adventure to save the philosopher's stone, and each of them received 50 points for it. Harry showed additionally, "outstanding courage" in the face of Lord Voldemort , which netted him the extra 10. Neville also showed "courage" in the face of his friends which netted him the same value as Harry, 10 points.