Network neutrality is a network design paradigm that argues for broadband network providers to be completely detached from the information being sent over their networks; it argues that one bit of information should not take priority, be prioritized over another. The implication is that the Internet, a network, is more efficient and useful when it is less focused on a particular audience and more attentive to multiple users.
As it stands currently, we have an open Internet – net neutrality states that Internet Service Providers (ISPs) should treatment all content the same no matter where it originates. As recent as last week, President Obama addressed net neutrality saying “The Internet should be a utility, just like electricity and water” (Obama, 2014). The president is asking that the Federal Communications Commission establish rules to ensure cable companies nor phone companies can act as gatekeepers, restricting what we can do or see online.
In contrast, a closed Internet is one in which a third party has influence in the manner content reaches the consumer. However, the fear is that if ISPs are allowed to do this they would demand that providers such as Facebook to pay them to deliver the content faster than other content providers. An example is the agreement between Netflix and Comcast, Netflix is paying the cable company to provide faster speeds.
In summary, according to net neutrality advocates a closed Internet would provide incentive to ISPs to slow some content and expedite others depending on whom is paying them. This would most likely result in a limited amount of services being made available and an increase in cost for content services. Most importantly, advocates believe that this would suffocate innovation.

References
Network neutrality (n.d.) What is Network Neutrality. Retrieved November 18, 2014 from http://www.ocf.berkeley.edu/~raylin/whatisnetneutrality.htm

Snider, M. & Yu, R., (2014). Net Neutrality – what is at stake? Retrieved November 18, 2014 from http://www.usatoday.com/story/tech/2014/11/10/net-neutrality-fcc-qa/18815843/