What does it mean when mining company commercials say that they are aggressively mining a resource?

They’re going for it full out. If it’s an open pit operation, they’re bringing in lots of equipment and working to open the pit and set up an ore processing plant.
In hard rock mining, they’re sinking shafts into the earth to expose the vein of ore, laying track, bringing in ore cars and mine tunnel locomotives, building roads to the mine/claim site, and building a ore processing plant.

It means they are raping the Earth.

It also (or perhaps mainly) means they want you to think they are going to increase their stock value soon, so (they hope) people who hear the ad will consider investing in their stock.

All of the above and…

They are now mining ore that has a lower yield. That means more energy usage, more pollution, more rock and soil displacement per unit of product.

It means they’re gleefully fist-fucking the environment for every last penny they can squeeze out of the Earth and leaving the mess for others to deal with.