As Calimero says, 'The Cloud' is a buzzword. The Cloud is in fact very solid being made up of millions of very real server computers backed by probably billions of hard drives for data storage.
If you use Gmail or almost any other e-mail system, or indeed this forum, you are using The Cloud - these posts are being stored somewhere online.
Most of these hacks involve users who will have failed to use adequate passwords, or have let them become known. And for most of us a hacker won't really be that interested in our nude photos.
For the typical computer user, like us, The Cloud can be useful to us personally in two ways. Accessibility and backup.
Many of these services allow you to synchronise data between devices (like Dropbox). What happens is that you create/change a file on a PC for example, it then gets copied up to your 'Cloud' account, and then copied back down to any other devices you have - phone, tablet, laptop. This is handy as you can save a file and then pick it up again on another device without faffing about with pen-drives or whatever.
Obviously as part of this strategy your file is also now backed up as it has been copied to another location.
Using The Cloud for backup is the same as using an external hard drive, DVD, etc. You are making a second or more copy to fall back to should you lose your 'primary'. Relying only on a hard drive on the shelf for backup does carry a risk - if your house is burgled or burnt you may lose both your primary (eg. the PC) and the backup. Any pro will tell you that any worthwhile backup strategy involves an offsite copy as well, and a Cloud copy is a good way to achieve this.
Are these Cloud solutions perfect? No; you should really keep some 'hard' backups too. But are generally better than nothing - the chances of your house burning down and your Cloud provider going bust or having a breakdown at that same time are really pretty slim.
There are plenty of free services out there but most are limited in some way, either by amount of space or functionality. I've used SugarSync for a few years now, initially free, but as I needed more space I paid. They have now stopped all free use I think. They aren't perfect but I haven't yet found a better solution for my needs, so I pay about £45/year for 60GB. As part of that they also keep the previous 5 or so versions of each file which is useful when I get things wrong
£45!! you say? Well, to put that in context we spend something like £200/year on printer ink cartridges, never mind the broadband fees, etc.