All living organism contain phosphorus. Phosphorus is an important element of live as a component for cell membranes, as an energy source, and for other bio-chemical processes.
Phosphorus is a very reactive component making it readily absorbed and generally available in aquatic environments as either an organic or inorganic phosphate.
Phosphates (PO4) can be created within the closed aquatic system or imported from the outside.
Phosphate as a by-product of mineralization of dead matter such as plants, bacteria, feces, uneaten food, algae, fish slime etc. are all internal contributors. 
Dead plant material or rotting food particles settle either on the substrate or within the filter. Rinsing filter materials and vacuuming the gravel at every water change can significantly reduce potential phosphate accumulation from these internal sources.
Replacement water can also contain phosphate, sometimes surprisingly high concentrations, even if RO units are in use.
Additives such as pH stabilizers or carbon, and frozen fish food are potential external phosphate sources. Avoiding phosphate containing products as well as testing of the replacement water for phosphates can further help prevent accumulation. If in doubt, additives, carbon, pH buffers, and the water should be tested and replaced if necessary.
Prohibiting phosphates from entering the water or from forming within the aquarium is the best safeguard from the harmful consequences of accumulating phosphates.
Inorganic phosphate or orthophosphate is the soluble form. It is readily available and quickly absorbed by plants. Organic phosphate refers to phosphate that is part of a cell structure or organically bound in other ways. Organic phosphate must be broken down by bacteria in order to become soluble orthophosphate.
The biggest source of organic phosphate is fish food. 5 grams of flake food can increase the organic phosphate level by 0.4 ppm. The filters and substrate have to be cleaned regularly before the organic phosphate is mineralized to inorganic orthophosphate.
Some marine and especially reef aquarium set-ups rely on less frequent water changes. The reason for one is a delicately balanced filtration based on live rock and/or the need for nutrient supplementation for coral growth, 
among others. To compensate for less frequent water changes a protein skimmer is attached, which will remove many proteins and waste particles that would otherwise be broken down to soluble orthophosphates.
Unfortunately, protein skimmers do not work in freshwater aquariums and can not be substituted for less frequent water changes. More than 90% of the phosphate contained in the aquarium is organic phosphate. The common test kit measures the inorganic soluble orthophosphate, not the organic form or the total phosphate content.
Generally the measurable phosphate level should be below 0.05 ppm.
Phosphates are often associated with algae growth. Algae will grow with phosphate present in ppb (parts per billion), indeed only a limited amount of phosphates are necessary for algae to grow. However if nitrates (nitrogen compound) are kept low (see Algone), high phosphate levels will not create algae growth. Without nitrates there will be no algae growth no matter how high the phosphate concentration.
Planted tanks have the advantage that plants are capable of storing and consuming phosphates. Plants can only take up in-organic orthophosphate, thus reducing the levels. Saltwater tanks can imitate that by planting macro algae into a refugium or sump.
In reef aquariums Kalkwasser can just about eliminate phosphate. At a pH above 8.9 phosphate precipitates in the water as insoluble phosphate and flocks out. Marine aquariums kept above a pH of 8.4 allow some phosphate to be bound to rocks and substrate in an insoluble form. Nevertheless it will become soluble if the pH drops below 8.
In closing, phosphate can not be removed from the water since organic phosphate is constantly converted into in-organic soluble orthophosphate. Nevertheless, phosphates can be controlled by a good maintenance schedule aimed at keeping organic phosphates and nitrates at a minimum.
