This is distinct from a cross-cloud approach, in which the same app runs in more than one cloud simultaneously.
The benefits of a cross-cloud strategy vary depending on which type of cross-cloud deployment architecture enterprises use.
In cases where a business deploys redundant instances of an app on more than one cloud, the main benefit is increased reliability.
In cases where different parts of services of an app reside in different clouds, the chief benefit is increased flexibility. This type of cross-cloud deployment makes it possible to pick and choose which specific clouds host which parts of the app.
This flexibility can translate to better performance and lower costs, as one cloud platform might better cater to the needs of one part of the app, while another cloud better fits the other part. For example, a company might have an app with services written in different programming languages. One service is written in a language that is natively supported by AWS Lambda, a service for running serverless functions. Another service is written in a different language that Lambda doesn't directly support.
The only way the business could run the service on Lambda is to use a runtime API, which is more complicated. So, it decides to host the first service on Lambda, while running the other on a different cloud with a serverless function that natively supports the service's programming language.