Gold is a purchasable currency that allows you to purchase Premium items in-game using your Microsoft Account and Billing information. Silver is an in-game currency that is gained through playing battles and does not require any real currency to obtain. Silver is not able to be converted into Gold, however, you can exchange Gold for Silver using the «Exchange Gold» option under the «Store» tab.
Using Gold does not give much advantage in battle, but it can significantly increase the comfort of the game. Progression within the game is reliant on Silver and Experience, more than Gold, so Silver is actually a more valuable asset to have.