Question

What was the significance of the battle of marathon

Answer 1

As the Persians sought to destroy Athens and was planning to land their ships at marathon and march to Athens. Getting word of the oncoming fleet, the Athenians called upon Phidippides to run the 140 miles to Sparta to ask for aid. 
Sparta refused to fight as they religiously couldn't when the moon was full. Although they did later come to protect Athens.
Phidippides then had to run all the way back (36 hours, mind you, to deliver the news) 

Even without the Spartans, Athens won the battle despite being outnumbered 1:4

the surviving Persians set sail for Athens and by the time that the tired Athenian soldiers arrived back home. The Spartans had come to their aid and defended the city.

It was basically the first instance of cooperation in the face of a military conquest against another city-state - in this case, where Athens received aid.

My favourite videos explaining this. (although history channel does tend to exaggerate, it's 1 to 4 in a ratio of Athenians to Persians)

http://www.history.com/topics/ancient-history/ancient-greece/videos/the-battle-of-marathon

https://www.youtube.com/watch?v=KgijJ-zdHow 
(if you want a giggle. "NOW WITH STATE OF THE ART VIDEO TECHNOLOGY")