Imagine you have built out an application locally for XYZ company. That application needs to run somewhere right.
So, one way is your company buys a server, and you along with your team manage the server.
If something goes wrong your you will have to quickly fix it as your company application is deployed on the server.
Another way is you delegate infrastructure management
i.e you get yourself relieved of the infrastructure management and give the responsibility to some organization. Now, this organization buys the server and manages all of it. This way you moved your infrastructure to the cloud.

So, using the infrastructure setup and managed by someone else is called infrastructure as a service
Eg AWS, AZURE, Google cloud platform, Digitial Ocean.