Water is formed from the combination reaction of hydrogen gas (H2) and oxygen gas (O2) 
to produce liquid water (H2O). In other words, each molecule of water is made up of two hydrogen atoms and one oxygen atom. Each oxygen atom in a water molecule is bound by a strong covalent bond to each of the two hydrogen atoms in a single water molecule. That is, the oxygen in liquid water is strongly bound to two hydrogen atoms forming water molecules. A fish therefore cannot break water molecules apart to get the oxygen. This simple means that the oxygen that fish breathe is not the oxygen found in water since it is not free to take part in respiration. Thus, since fish cannot breathe the resulting liquid water, the oxygen gas (O2) that the fish breaths comes from that which is dissolved in the water.
Hence, fish “breathe” the dissolved oxygen out of the water using their gills. Fish gills are thin feathery membrane structure that allow water (containing dissolved oxygen) to move between the layers and enable oxygen to diffuse into the fish’s bloodstream. A fish’s gills take oxygen from the water the same way human lungs extract oxygen from the air. 
This also means that if there is not enough dissolved oxygen in the water, then the fish can suffocate, just as humans and other animals will if there is not enough oxygen in the air that we breathe.
