Instagram App was launched in October 2010. At that time there weren't so many Apps on the Apple App Store. It's believed that this fact helped Instagram. See how Instagram started.
Before it's launch the founders had $500,000 of funding to finance their Initial App Burbn. As the founders moved from Burbn to Instagram it's believed they used the money to push the initial downloads. See how Quora gained traction.
As people were allowed to post their Instagram pictures on Facebook others discovered the App and wanted to use it to take photos. See why Instagram is popular.
The Iphone 4 was released in June 2010 with a much better Camera. This helped Photo taking Apps such as Instagram to boom. See Why Facebook bought Instagram.
Instagram used Facebook's social graph extensively. People were allowed to sign using Facebook, to import their Facebook friends and to share their posts on Facebook. See how Facebook started.
Instagram was initially released for iphone. As iphone sales exploded with the release of iphone 4 Instagram downloads were pushed. See why people love iPhones so much.
Jack Dorsey, the founder of Twitter, twitted about Instagram in its early days to his 1 million+ twitter followers. Kevin Systrom , Instagram's founder, used to work with Jack Dorsey in the company Odeo. See how Twitter started.
Celebrities such as Justin Bieber, phil schiller and others started using Instagram. This helped the App become even more popular. See why Celebrities use Instagram.
Existing social networks such as Facebook had photo uploading capabilities but didn't have any editing options like the filters. People were basically using Instagram to edit photos before uploading them to their preferred social networks. See why Some people hate Instagram filters.