Taken from the Players guide:
Each asset a player controls is worth a certain number of points. The score sheet shows the current tally of points for each asset and how you fare against other players based on the point total. It also lists the victory conditions and shows how you close you are to reaching them. If the host chose the Public Player Scores option during the game setup, score statistics for all players are shown after the first 20 turns have passed.
=> Click on Switch to toggle between the score/rank, victory conditions, and a history graph.
Here's how empires score:
Planets: From 1 to 6 points, scoring 1 point for each 100,000 colonists
Starbases: 3 points each (doesn't include Orbital Forts)
Unarmed Ships: An unarmed ship has a power rating of 0. You receive 1/2 point for each unarmed ship (up to the number of planets you own).
Escort Ships: An escort ship has a power rating greater than 0 and less than 2000. You receive 2 points for each Escort ship (up to the number of planets you own).
Capital Ships A Capital ship has a power rating of greater than 1999. For each capital ship, you receive points calculated by the following formula: Points = (8 * #_capital_ships * #_planets) /( #_capital_ships + #_planets) For example, if you have 20 capital ships and 30 planets, you receive (8 x 20 x 30) / (20 + 30) or 4.8 points for each ship.
Tech Levels: 1 point for levels 1-3, 2 points for levels 4-6, 3 points for levels 7-9, 4 points for level 10 and above
Resources: 1 point for every 30 resources