Functionally, under the hood, they *do* the same thing: they act as a management tool between the user and the hardware. Without getting too geek about it, the two systems do it very differently.
The major "difference" from the user perspective is the user interface. Windows has a single interface, which usually changes only when a new version is released. There's a single desktop and a limited amount of ways to customize it. Linux (which really describes the operating system "kernel" that does all the work under the hood) is distributed with different interfaces and GUIs: Gnome, KDE, Xfce, Enlightenment, etc. These are all very customizable and you can usually find one to suit your needs.
The other big difference, obviously, is software. Linux doesn't run Windows software and visa versa. There are many application that have both Linux and Windows versions (Adobe Acrobat and Flash are two that come to mind) and many open-source application developers make their apps available for multiple platforms (Apache Web server, many programming languages like PHP and Perl, many user apps).
There are ways to run Windows software on Linux, through the use of virtual machines or tools like WINE. They have their advantages and disadvantages.
Subsequently, there are many Linux-capable apps, nearly all open source, that perform the matching functions of Windows apps. OpenOffice is the primary office suite like Microsoft Office. GIMP is the main graphic app, like Paint Shop Pro or even Photoshop. Firefox is the primary browser. There are lists on line of apps that perform various functions in Linux versus their Windows counterparts. Here's one:
http://laptoplogic.com/resources/top-50-linux-alternatives-to-popular-apps
The argument that Linux is hard to use makes no sense with todays Linux distributions. Linux is no more difficult to install, configure and use than any other system. The reason that many people find Linux distros "difficult" to install is because they've never installed an operating system. Most people buy computers with Windows pre-installed...this isn't common with Linux. This is why you see a lot of confused questions here about reinstalling Windows...people just can't seem to do it right a lot. On most of the popular distributions (the Ubuntu family, Fedora, PCLinixOS, Mint), you can manage the installation in a matter of minutes.
The two key things to remember about Linux are that it's free (free as in freedom and free as in free beer), and they you can use it side-by-side with Windows. If you have Windows installed on your new laptop, you can install nearly any version of Linux on the same system in a dual-boot format, in a separate partition, and you can choose which system to use when you start the system. This is the preferable way to run Linux and Windows together, in my opinion. You can also use VMware and other virtual machines and there's even something that allows you install Linux within Windows and run it from there.
Many Linux distributions come as LiveCDs, which means you can burn the ISO images to a CD and run the system from there by booting to the CD. This gives you an opportunity to try it out in a limited way before installing it.
I've answered tons of questions here about Linux over the months, so feel free to browse through my previous questions in my profile to get more information. This is not a question easily answered in one shot.