Cloud-First, Mobile-First is not your business strategy, is "their business strategy".

Is it good? is it bad? Yes it is good, the cloud will help business to reduce costs and driving your applications to mobile device it is also good because your customers will interact with your business by using the "new PC" called "SmartPhone". But Cloud-First and Mobile-First it is not a business strategy for your business, it is a business strategy for IT Vendors (HP, Amazon, IBM, Microsoft, others...). 

There is no doubt, no question about it, all major IT vendors are on a "Cloud-First, Mobile-First". It don't even deserve explanation. It means trying to move all data to a cloud and all application to a mobile device.

Cloud-First is an evolution of outsourcing, when you move all that servers, apps and things that your don't understand (the stuff that IT people loves) out of your company, since your company is not making profits by having servers and paying for software itself.  It provides your company cost reducing benefits, but it is not a business strategy, just by putting you application on "the cloud" it does not mean you are going to make more money. And you can save some money but you need to make the numbers fit, it is not that you are going to save money like magic, maybe you need a migration, prepare your applications, invest more to go the cloud. So make your number rights, the cloud may assist you on reducing costs, but it is  not going to help you make money by itself. There may be examples on how to use the cloud to get more customers and more sales, but those are specific strategies and not just "The Cloud".
I remember hearing an IT salesman that it does not mean that all is going to be on the cloud and that it is expected that on companies will have a 50%/60% stuff on the cloud and the rest "on Premise". So, when we reach that day, the hype of the cloud will be over and IT vendors will be looking what is the next big things to offer.

Mobile-First, just sucks... why? Because as a IT people we already migrated from the mainframe, (centralized applications) to client-server applications to Unix. Then we migrated from Unix to Windows and migrated all applications to run on Windows. After that we thought that it will be better to migrate all to the web (client-server with a browser) and return to centralized applications. And now that the mobile smartphones worked so good, we (The IT guys) want to make more money by migrating you applications to iPhone and Android. What?. So for IT Vendors Mobile-First it is just an strategy to make you migrate to other technology again.

But don't get me wrong, a Mobile-First, strategy can really help you make increase sales if you really know your customers and if you product requires and gives value to an "always mobile" person. A banking payment tool may be a success on a Mobile-First strategy, since people want to be able to pay debts "on the go". But if the bank only wants to offers a view of your account without any ways to take action your money on that case maybe a Mobile application is not required at all.

From the technical point of view, creating stand-alone (client-server) applications for mobile phones on iPhone and Android is just getting back to the days that you have only Windows on the PCs . People that used MacOS or OS/2 was given the cold shoulder because they were a minority and developers didn't want to do application for those platforms, only Windows that had all the market share at that time. At some point developers and customers started to think that they need to be "platform independent" and moved applications to the web on open standards so it didn't matter if the final user has Windows or any other platform, he just required a browser that supported the web standard.  So, this is why smartphone developers are trying to do "hybrid" application development that with a few changes it will run on iPhone and Android. So maybe in a future we will be migrating the iPhone/Android apps to a more "hybrid" approach or maybe back to the web.

So Cloud-First and Mobile-First are real things that are happening today, we should not hide under a rock and/or ignore it. Using the mobile is a way to reach more customers, and using the cloud helps to save costs, but each case needs to be analyzed. Today the cloud and the smartphone are on the peak of the hype, but you always needs to put the strategy and numbers over the table first.