Firstly, a word of warning. The information in this post is accurate in the current beta build 15913 and may change significantly before launch.
So first, let's look at the more complex of the two battlegrounds, the Silvershard Mine. As the name would imply, it's in a mine. Revolutionary! More specifically, it's in a Venture Co. goblin mine underneath Stranglethorn Vale. It's described in the battleground finder tool as a 10vs10 escort battle, which is pretty accurate, as the objective of the battleground is for each faction to capture and escort mine carts to depots at the end of the line, retaining control of the carts throughout their jouney from the central depot to their destination. An added level of involvement is found at the crossroads, where players can change a mine cart's direction.