Archon is a Chess-like game where the pieces "battle" for squares in an action arcade sequence. The goal is to either destroy every one of the enemy's units, or capture the 4 "power points" on the board.
While the two sides, the Light and the Dark, have similar units, their arcade sequence abilities are different.
Half of the board is made up of static black or white squares, while the other half of the board have squares that change color each turn. In the arcade sequences, Light units are stronger on White squares, and Dark units are stronger on Black squares. This relative strength difference manifests in a larger hit point pool for the unit and stronger attack power. Regardless of the underlying square color, some units are naturally stronger than other units.
At the beginning of the game, the color changing squares start in a neutral "gray" color, which means units battling on them are at their base strength. Each turn, the changing squares slowly rotate towards full "White", then rotate back down towards full "Black". As two of the 4 power points are located on these changing squares, it's an important strategic goal to make sure your stronger units claim the power points when the color rotation swings towards your side's faction.
Similar to Chess, units can move in different directions (or fly over other units) during the turn based phase. When two units are moved onto the same square, the action phase begins.
During the action phase, the game board disappears and is replaced by a battlefield strewn with obstacles. After a brief countdown, the battle begins, and the players control their unit by moving them in 8 directions and using their attack. There is only one type of attack per unit.
While the two factions have similar units in the turn based mode, during the action mode they usually have very different (but balanced) attack modes. For instance, the Light Side has a Phoenix which has to stop moving to perform it's limited range Area of Effect "explosion" to damage the enemy, while the Dark Banshee can slowly move while engaging it's weaker AoE "Scream" attack. The Light Side Knight has a strong melee attack and higher health than it's equivalent Dark Side Goblin - but the Goblin is faster and it's melee attack has a longer range.
Additionally, some units can fly over the obstacles on the battlefield, and some units have projectiles that ignore the obstacles.
Depending on the skill of the player as well as the "color" of the square the units are battling on, it's possible for very weak units (such as the Goblin) to defeat much stronger units (such as the Golem).