When writing applications, libraries, or other source code we often want some control over how it is used by the community. Licenses allow us developers to protect our rights to the source code while defining the terms in which others may utilize it. Two of the most common licenses used in open source software are the MIT License and GPL License. Although similar in that the they both allow users to utilize, modify, and redistribute the code there is one main difference between these licenses. That difference is that the MIT License is permissive and the GPL License has strong copyleft.
Although it may be confusing at first which library you utilize comes down to whether or not you want to allow the use of your code in proprietary software. The MIT License gives this permission under the stipulation that the License is distributed with that software, while the GPL License only grants use and modification by non-proprietary software.
As the copyright holder of the software you may decide you want to Dual License the software with both licenses allowing users to incorporate your source code into their own software under which ever license they want to use. This is also a viable option and is used by such libraries as JQuery.