To supplement what HVS said, interstitials which appear before, say a homepage loads, are very much there for the purpose of advertising, we've all seen the 'close this ad' link.
One instance where they can be helpful from a user experience point of view is when a user initiates an action which requires feedback from a process which may take some time to respond - either because it's slow, busy or just has a lot of processing to do.
Think of a site where you book a flight online for example. You often get an interstitial on hitting 'find flights' because the the system is having to go off and ask for all relevant flight information and then sort them for you before displaying them on your screen. If this round-trip of 'request, interrogate, return, display' is likely to take an amount of time beyond that which a normal webpage transitions from one to the next, a UXDesigner may consider an interstitial screen (or message) to let the user know something is happening whilst at the same time allowing the system the time it needs to complete the request. Any screen with this sort of face-time is going to get the attention of your marketing department from a 'well while we've got them we might as well show them something' point of view.
As a UX Designer myself interstitials like this are not always preferred as I'd love every system to return data immediately but if it can't for whatever reason, I'm very much for keeping the user in the loop as much as possible about what is happening - rather than leaving them to stare at the browser status bar until they either try again or get fed up and leave.
One final point when considering this is also to have a lower and upper time limit on a screen like this. If you need to show an interstitial, show it for long enough so people can read it and understand it but not too long that they get fed up of waiting. As a rough guide, leave it open for at least 3-4 seconds (even if the process averages 4 seconds but has finished after 1 on this occasion). Between 4 and 10 seconds check every second to see if the process has responded (and then take the user to the next page f it has) and after 10 seconds seriously consider telling the user to either try again or telling them you've failed (whilst at the same time getting your tech team to fix what is ultimately a problem which will affect your bottom line).