What does "spooned and leveled" mean?

The easiest way to measure a cup of flour is of course to take the measuring cup, plunge it into your bag of flour and just lift up a spoonful. The problem with that is that the plunging and lifting will compress the flour inside the cup and actually get you more flour than you wanted. If you spoon the flour into the measuring cup you minimize the compression and will get a more accurate measurement.

You're exactly right, it means to spoon the flour in and then level it off.

If you scoop the flour, meaning you dip the measuring cup into the canister and scoop a large amount out, the pressure compacts more flour into the measuring cup. When you spoon it into the measuring cup instead, the flour is less compact (so there is less of it in the same 1 cup measure). Subtle differences like this can mean a big difference in the end result when baking.

If you were to measure 1 sifted cup, 1 spooned cup, and 1 scooped cup on a food scale you would get three different results (from lightest to heaviest). This is why I'm a big fan of recipes which use weight measurements for the ingredients.

I would recommend getting a gram accurate scale and using the weight listed on the side of your bag of flour. If you are baking then you really should be weighing your ingredients. If you aren't baking, then you can probably get by with the "scoop and sweep" approach since accuracy is actually not required.