Question

How did photosynthesis lead to the development of animals living on land?

Answer 1

Around 2.4 billion years ago, the first photosynthetic organisms appeared and used inorganic matter like carbon dioxide and water to produce glucose, with oxygen released in the atmosphere. Because of this, oxygen levels rose; this is called the Great Oxygenation Event. Through time, photosynthetic organisms evolved to live in land (now as plants). As concentrations of oxygen in the atmosphere became higher, marine animals evolved to utilize oxygen readily available from the atmosphere (rather dissolved in water) hence the evolution of marine animals to land animals capable of respiration in land. 

Answer 2

Photosynthesis was essential for filling the Earth atmosphere with oxygen that is necessary for metabolic processes of all animals.
Only after the plants colonized the land and raised the levels of oxygen in the atmosphere to levels high enough to sustain animal respiration did the animals move from aquatic to terrestrial way of life.