The Player Status is shown in the lower left corner of the battle screen.
Your status is on the left. In this example you are grug and your opponent is Altren..
Flux: This is how much Flux each player has currently. In this example you have 4 Flux and the other guy has 6.
Domain Level: This is how what domain levels each player has. Right now you have 2 Dark Legion and your enemy has 2 Sylvan.
Other Player's Last Action: This is the last action performed by your opponent. In this example he used his Trunk Hermit to attack your Ghost Crypt. You can mouse over these icons to get details of what did the action and what it did it on.
Glory: This shows how much Glory each player has. The first player to get 20 glory wins the game. Whichever player controls the most flux points at the end of the turn gains a Glory. Above you have 0 Glory and your enemy has 4.
Current Player Glow: TWhoever's turn it is will be highlighted with this glow. You can still build actions when it isn't your turn but they wont take effect until it is your turn. See Turn System.
Action you are Building: This is the action you are currently building. It will show the icon of the thing you are causing to act and the action's targets. Here you are building a Bone Fortress in the plains.
Pass Button: You can use this button to toggle between the Passed and Unpassed state. When both players have Passed the next round starts. See Turn System.