Publish
Publish means, that you make the model available for the public, that also contains the fact, that it can be viewed over the Process Portal by everyone who is authorized. It can still be modified after publishing, so it is not write-protected. If it has been modified you simply have to reload the Process Portal and the new version is shown, it is not required to publish the model again.
Preview
Preview does the same as publish, with the exception of the display in the process portal. The model is not shown on the normal model explorer on the left side of the Process Portal. But if you have the specified link to a preview model you can still view the model over the Process Portal, you just need the direct link to the model. This might be helpful when there is a group of people who should have the possibility to view it over the Process Portal but for all other people, it should not be available. So only the authorized people get the link to the model, therefore it is avoided that unauthorized people have insight.
Approve
With Approve the model as it is will be available for the public and is read-only as soon as it is approved. All modifications which are made afterward are forced to save the model in a new version. So, the approved version is final and can't be changed anymore. Approving a model will not make the model available in the Process Portal.
Reject
If you want to reverse the approved model, then you need to use the Reject action. But please note, that even with the rejection, a new version will still be forced when making modifications.
Hide
With Hide, you can make your model invisible despite the fact that it has been published and therefore is displayed in the Process Portal. So, if you published a model and have to modify that model but you want that the old version can't be viewed by anyone, then you simply hide it until the new version of the model is finished.