Open source software is simply software that has its source code available for anyone to download, see, modify and create new programs based on it as long as those new programs also stay open source. In this way, everyone is free to modify it to his own needs and develop it in any fashion he wants. Absolute majority of these programs comes free of charge, but without support from the vendors. The open-source software has recently gained popularity in governmental and commercial sector, especially in some European countries.
Apart from the obvious advantage it has over the programs you need to pay for - that it comes free of charge, open-source software has other good sides as well. First of all, it is the availability of applications - for almost any program you can find an open source alternative (or a couple of them). For example, instead of using Microsoft Office you can use Open Office, instead of CorelDraw you can use Inkscape, instead of Adobe Photoshop - Gimp, instead of Internet Explorer - Mozilla Firefox or Chrome etc. And these programs can do everything (or nearly everything) you previously did with your old software. The fact that the code is available for everyone has another advantage - the bugs and security problems are fixed faster because there is a large community of programmers all over the world who work on these problems. Because of that these programs stay stable and secure for the end-users. And finally, if you have any problems you can ask for help from the community of users and developers of these programs and usually you should get help quickly.
On the other side, not everything is great about the open-source applications. To begin with, in most cases they do not come with support from the developers so you can rely only on the community to help you, and that is not enough if you really have a problem which has to be addressed urgently. Furthermore, since you did not pay for anything, you cannot complain if the software does not work, if it crashes or you lose data.