Synthetic leather is intended to look and feel similar to actual leather without the ethical concerns about animal rights. That's just one of several benefits to wearing faux-leather shoes instead of actual leather.
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Synthetic leather is frequently used in vegan shoes and other brands that cater to those concerned about the welfare of animals. Faux-leather is frequently made of a combination of textiles and polyurethane to give the synthetic material an authentic leather feel. Genuine leather also has to go through extensive treatment to make it ready for shoe manufacture and the chemicals used to treat it have been found to damage the environment and take away the biodegradability of the leather. Synthetic leather shoes, on the other hand, don't require as much preparation and use less chemical treatment.
Traditional leather tends to be much more expensive than its synthetic counterpart because leather requires much more preparation and is therefore more expensive to prepare. The cows needed to make leather require care, land and food and then the cow skin has to be treated before a shoe can even be made. All of this contributes to the eventual cost. Synthetic leather doesn't require as much preparation or labor to produce and therefore faux-leather shoes are usually significantly cheaper.
Synthetic leather shoes are designed to retain their form and are usually very durable. They're also more water-resistant than real leather, which can stain and suffer damage when exposed to the elements. Synthetic leather is designed to hold up against weather conditions and the wear and tear of walking and running over an extended period of time.