An On-Premises Network has all of the resources located in your office. Your servers, network storage, email services, phone systems, and other hardware are all located in your office. This is the preferred method for most medical professionals and legal professionals, who need to take extra measures to ensure data is not compromised, and have to follow legal compliance requirements.
Hybrid networks are the most common configuration. Some resources (servers, storage, etc) are located in-house, where other resources (email, phone system, communications servers) are hosted in the cloud. Many businesses prefer the convenience of having certain features cloud-based, while still enjoying the safety of having on-premises servers and storage.
A Cloud based solution relies more heavily on cloud-based services than a hybrid network. In a Cloud network, typically the only pieces of hardware stored on site are routers, switches, and access points. Other devices, such as servers, domain controllers, and application servers, are all hosted in the cloud. If you have many employees working from home, this may be the way to go.