Why is it important to understand if an organization is based on a centralized or decentralized organizational structure?

Mostly because you need to understand the chain of command.
In a centralized organization, the decision making process fall to the hands of a very few people (in some case, it even can fall to one person) , which mean all level of managers can't move freely without the decision maker approval.
In a Decentralized organization, all different managers from different divisions have the authority to make decision

Wavelength divides in half and speed stays the same.