Let us use the analogy of an apartment complex. When you are renting an apartment in the building, you are an integral part of the main structure. You may utilize some common areas such as the lobby and elevators but once you reach your apartment; you are in your private area. You can create the interior space as per your choice as long as you are not impacting the structure of the building.
In a Public Cloud
, a single host (similar to the apartment building) will support multiple customers but will make sure that their specific resources (like items in the apartment) are not shared with other customers. Just like with an apartment building (one bedroom, two bedrooms), you can rent computing power, storage, and network resources based on your needs. Basic services to support everything beneath the operating system layer is typically offered by the Public Cloud Provider.
A Private Cloud
on the other hand, well, is more private. Each private cloud customer is supported by a dedicated host(s). To continue with the analogy of an apartment building, a penthouse with its dedicated elevator, special security and certain other privileges makes it quite different from the other apartments in the building complex. Nobody stops you from creating your own Private Cloud in your data center, but you will probably not do that if you are looking to have someone else take care of the IT infrastructure so that you can focus on your business.
As you have already guessed, Hybrid Cloud is a combination of Private Cloud and Public Cloud. It is like having a penthouse and then a few apartments, not because you ran out of space in the fancy penthouse, but for other reasons such as cost, long term plans, or other specific requirements.