Fluxbox vs LXDE
Fluxbox is a window manager, and LXDE is a desktop environment which includes a window manager. Both are intended to be simple and lightweight. So they're suitable for slower computers.
For the non-expert, the best way to see them in action is to download a Linux distribution built with one or the other - such as Lubuntu 11.04 or Linux Mint 9 'Fluxbox'.
Both of these distributions are based on popular, user-friendly Linux distributions (Ubuntu and Mint). But by using a different window manager than the default, they sacrifice some in terms of their ability to work with the latest-and-greatest software and features. For example, drag-and-drop on the desktop or file-manager may not work. It may be difficult to get the machine to log in to the desktop automatically or to connect to a wireless network without demanding a password. Interactions between programs and the desktop environment may not work the way you expect.
[edit] LXDE
LXDE more widely used than Fluxbox. Each of these popular linux distributions has been made available for download with LXDE installed (either as an "edition" or as a "new distribution"): Ubuntu, Mint, Fedora, Debian.
Because it's more widely used, LXDE tends to attract more developers and more of the issues that would make it difficult to use have been solved. (Or at least, a workaround has been posted publicly to the internet.)
[edit] Fluxbox
Because of its small memory footprint and quick loading time, Fluxbox is popular in distributions focused on maintaining a small-footprint, utilizing lightweight applications and is ideal for machines with less memory or older processors. It is currently the default window manager of PCFluxboxOS, a remaster of PCLinuxOS, of Linux Mint Fluxbox CE, and of Fluxbuntu, an Ubuntu derivative with lightweight applications. Additionally, it may be installed on most popular distros (ex. apt-get fluxbox; pacman -S fluxbox; yum install fluxbox, etc.) and selected from the KDM/GDM/LightDM Login Managers session menu.
Fluxbox is very customizable and offers good documetation, though is more suited for more advanced users who are comfortable using the command line. Configuration is handled by editing configuration files. This method, while extremely flexible, requires the user to learn the appropriate syntax to make desired changes. Unfortunately, becuase fluxbox lacks the user base of more popular distributions it is often more difficult to find support, hence it requires users to become more familiar with the documentation and associated configuration commands than other window managers. That said, the configuration files are easy to understand and there are many fluxbox "styles" available. Fluxbox offers window tabbing, layering, hotkeys, and other impressive (and minimalistic) features.
A potential user should weigh fluxbox's very small footprint against fluxbox's somewhat more complicated setup.