For a better updated version of this tutorial please visit: https://www.instructables.com/id/How-To-Use-Mocap-Files-In-Maya-BVH-or-FBX/

This tutorial is made for Maya 2013, but I believe it should work in 2010-2015.

If you are using a bvh file, download autodesks free bvh converter and convert it to an fbx file and follow the fbx instructions.

https://usa.autodesk.com/adsk/servlet/pc/item?siteID=123112&id=22694909


For those with an fbx file, first make sure that the maya fbx importer plugin is loaded by going to WINDOW->SETTINGS/PREFERENCES->PLUG-IN MANAGER  and checking the box to load the fbx importer (for me it is called fbx maya).
 


Now, import your fbx file using FILE->IMPORT.
Once your fbx is loaded, go to the animation menu set and then select SKELETON->HUMAN IK 

Now select the root joint of your rig and then in the character panel (on the right) select the dropdown menu (the picture of the man in a circle) and then click on DEFINE->SKELETON
 

Now, in the character panel navigate to the definition tab and select a joint and then select it's corresponding joint on your rig. Now right click on the joint in the character panel and select assign selected joint. 

Do this until you have all of corresponding joints from your rig mapped out. Repeat the procedure of defining a skeleton and then mapping out the joints with the motion capture character skeleton. Now in the character panel,  simply select your control rig in the character drop down menu and then select your motion capture rig in the source dropdown menu.


If you did everything correctly, when you press play your character should move the same as the motion capture rig.