In a resource management game, the main mechanic is for the player to collect resources that can be used to build things, upgrade, or accomplish the goals of the game. Resources can be money, heat, corn or other crops, oil, gold, steel or other metals, wood, sheep, etc.
One famous game is Settlers of Catan where your workers collect sheep, wood, wheat, clay and ore. When you have enough of these resources through resource gathering or trading with other players, you can use them to build roads, settlements, cities and collect development cards.
Another game that uses resource management is Scythe. Here you start with a character miniature and 2 workers. The workers move to different hexagon shapes and can collect resources on whatever a certain hexagon provides.
Resources include other workers, oil, food, wood, and steel. The resources you collect go on the board with the worker. You can then use them to build Mechs that transports workers and attack other players, upgrades, buildings (granary, mine, windmill, and monument), recruits which gives bonuses.
The idea is the build and upgrade as much as you can to collect stars. Like building all 4 buildings will give you a star. Upgrading everything on your player mat also give you a star. Collect 6 stars to end the game and count your points.
Another Resource Management game I like playing is Terraforming Mars. Here you have to terraform Mars by increasing the temperature, oxygen levels and using all 9 ocean tiles on the board.
You have a player card with resource production. Each generation, you produce resources like megacredits (aka money), steel, titanium, trees, energy, and heat. It depends on your level of production that you can increase through use of cards. You use these to terraform Mars and collect victory points. If you produce 8 trees, you can use those trees to place a forest tile on the board witch increases the oxygen levels. Use 8 heat to increase the planet's temperature.
You can also use your mega credits to produce standard projects. Like if you don't have enough trees, you can spend 23 mega credits to build your forest the board. There are cards that require resources and mega credits as well.
There are many more resource management games like Splendor, Puerto Rico, and more. It is still a popular game mechanic.