This allows you to check how are you expending money in AWS services and help you detecting anomalies.
Moreover, you can configure an anomaly detection so AWS will warn you when some anomaly in costs is found.
Budgets help to manage costs and usage. You can get alerted when a threshold is reached.
Also, they can be used for non cost related monitoring like the usage of a service (how many GB are used in a particular S3 bucket?).