Plants need about 16 elements to grow.
Some they need a lot of.
Some they need just a little.
Some of the things that we add to our tanks for other reasons also supply the plants with some of the things they need.
Hydrogen (H), Oxygen (O): A tank without hydrogen and oxygen may be safer according to the dihydrogen monoxide believers, but I prefer a tank filled with water.
Carbon (C): Most plants need carbon in the form of Carbon Dioxide. When they take in the carbon they start making other molecules with it, and someone figured out that they could supply the plants with carbon in the form of those molecules instead.
The next three are macros, and are the real, legal definition, fertilizers:
Nitrogen (N): Found in proteins, so fish food is one source. We measure Nitrogens as ammonia, nitrite and nitrate. Plants can use all three, but do not use fish food directly. It has to break down into ammonia. Often added to a planted tank in the form of KNO3, potassium nitrate. If your aquarium tests are already showing you have a lot of NO3, then you do not need to add more, but find out where it is coming from (tap water, fish food, other)
Phoshorus (P): Usually supplied as phosphate, comes in fish food. If you have enough nitrate from fish food you probably have enough phosphate, too. If you have to dose Nitrogen, then you probably have to dose phosphate, too.
Potassium (K): Aquarium plants seem to use a lot of potassium, and its supply in fish food is not as reliable as N or P. Even if you do not need to dose much else, I would dose K.
The next group are secondary nutrients. Plants need less of these than the ones listed so far.
Calcium (Ca) and Magnesium (Mg): When you test the GH or General Hardness Ca is one of the minerals tested, Magnesium is the other. Most tap water has enough of each, but very soft water might not. Most plants use Ca and Mg in a ratio of around 4 parts Ca to 1 part Mg. The ratio in the water does not have to be exactly that, though. Just so long as neither is zero. There are separate tests if the GH test shows the level is so low that you are suspicious of a problem. If you need to dose both, GH Booster is good. If you need to dose either separately there are materials to do that.
There are a few other minerals that are secondary, but are almost never in short supply.
Micros, the elements that plants use the least of are usually simply dosed as a group, in a blend.
Iron (Fe): Used by plants and not as often available from fish food. If you only needed to dose a couple of things, one of them would probably be iron.
Dosing macros as a blend that includes iron, if you test at all, just test for iron. Keep the iron in the right range, and assume all the other macros are fine.
Carbonates: Not an element, but the other most frequently discussed aquarium parameter:
Carbonates and bicarbonates are a buffer that stabilizes the pH. Low carbonates and the pH is more likely to vary. High carbonates and the pH is more likely to be high.
Roughly half the plants we grow in aquariums can use the carbonates as a source of carbon.
Nitrifying bacteria get the carbon they need from carbonates.
If you need to add carbonates there are several materials to do this. Baking soda is one of the most common.