Mark Zuckerberg said in a post 'Now, we'll be able to work even more closely with the Instagram team to also offer the best experiences for sharing beautiful mobile photos with people based on your interests'.
As many people started sharing pictures on Instagram instead of Facebook it became evident to Facebook that buying Instagram is an important decision. See Why is Instagram popular.
Facebook's Mobile App is more complex than many other Apps, including Instagram, and this makes the App less competitive. Facebook might have wanted a simpler experience for mobile users.
In a later talk Mark Zuckerberg said that Facebook forced people to use Messenger because he believes that each App can do one thing perfectly. This might be one reason he bought Instagram.
Facebook wants to be in control of all the pictures people share. This was one of the reasons that motivated them to buy WhatsApp for $19 Billion dollars.
As Facebook's News-Feed became more negative more people moved to Instagram to see pictures of others without the noise.
Facebook wanted to dominate the social networking market. That's one reason why they also made a bid for Snapchat.
As many Celebrities started using Instagram Facebook could have believed that Instagram is becoming a threat, See why Celebrities use Instagram.