Here is a general overview of the Battle Screen.
Flux Control Bar: This shows how many Flux Points each player controls.
Players Status: See the Player Status page for more details about this.
Cards in your hand: This is the cards that you have available to play. You wont always be able to play these cards since you wont always have the Flux or the proper Domain Level that they require.
Cycle Card Button: This allows you to discard a card in your hand. You wont draw a new card at the end of a round if you have 7 or more cards so this is useful if you want to get a new card.
Card Details: See the Cards documentation page for more details about this.