Lanterns are used to upgrade your Master Thief, unlock various units, and buying up to 3 victory points. When you unlock a unit with lanterns, you get one of that unit for free, so you can substitute lanterns for gold in certain situations as well. More valuable early game, with moderate value late on for situational responses.
Gold fuels your turns and actions. It allows you to buy units to do what ever it may be you need done on your turns, be it upgrading resource income, stopping your opponent, or taking an objective. Without gold your turns and progress can start to stall and give your opponent an advantage or leave you without an answer. Valuable early one, but essential as late game approaches to secure objectives.
The resource that allows all of your units to act each turn. All units have a single action on your turns with the exception of the master thief, which starts the game with 2 and caps at 5. Moving a unit on the board does not consume an action (thugs guard to the first tile they’re moved to).
How you win the game. Each map requires a certain number of victory points to end the match, 5 for the smaller maps (Wharf and City) and 6 for the larger ones (Masquerade and Palace). Objectives to award these include: filling churches, killing contracts, buying bribes, and whatever is the map specific objective if applicable.