By default, VirtualBox uses a technique called "software virtualization" to run a virtual machine on your guest computer. In a nutshell, this means that the code in the virtual machine (the guest operating system and other programs installed in the virtual machine) is allowed to run directly on the processor of the host, while VirtualBox employs an array of complex techniques to intercept operations that may interfere with your host.
In those cases, VirtualBox needs to step in and fake a certain "virtual" environment for the guest. For example, if the guest attempts to access its hard disk, VirtualBox redirects these requests to whatever you have configured to be the virtual machine's virtual hard disk -- normally, an image file on your host.
VirtualBox has very sophisticated techniques to achieve this without any special hardware. However, modern Intel and AMD processors have support for so-called "hardware virtualization".
The virtualization technology built into AMD's 64-bit processors is called "AMD-V" (originally referred to with the "Pacifica" codename). In addition, starting with the Barcelona (K10) architecture, AMD's processors have been supporting nested page tables, which can accelerate hardware virtualization significantly. VirtualBox added support for AMD's nested paging with version 2.0.
Intel has named its hardware virtualization VT-x (it was originally called "Vanderpool"). Support for nested page tables, called "Extended Page Tables" (EPT) by Intel, will be shipped with the new Nehalem processors and will be supported by VirtualBox in a future release.
While VirtualBox does support these hardware features, they are optional: you can enable or disable hardware virtualization individiually for each virtual machine.
In fact, depending on the workload, VirtualBox's software virtualization may even be faster than hardware virtualization. Other virtualization products that require hardware virtualization are usually much less sophisticated and tuned compared to VirtualBox. With VT-x and AMD-V, a special CPU environment has to be entered in order to execute guest code and whenever activity of the VMM is required, this environment has to be left and then entered again. This can be an expensive operation and in many circumstances, the benefits of hardware virtualization may not outweigh the performance penalty.
On the other hand side, with hardware virtualization enabled, much less virtualization code from VirtualBox needs to be executed, which can result in a more reliable system. So if you run into problems, you may want to try enabling hardware virtualization.
Enabling hardware virtualization is required only in two scenarios:
for certain rare guest operating systems like OS/2 that make use of very esoteric processor instructions that are not supported with our software virtualization and
if you want to run 64-bit guest operating systems (a feature added with VirtualBox 2.0), since most 64-bit CPUs ship with hardware virtualization anyway. The exceptions to this rule are e.g. older Intel Celeron and AMD Opteron CPUs.