PCI-X is an evolution of the existing (and rather outdated) PCI bus, used in the majority of all computers in the world today. The PCI bus is what is used to connect add-on cards like a sound card, a network interface controller (NIC) or an older graphics card. Newer graphics cards (for 3d graphics) usually don't use the PCI bus but rather the Accelerated Graphics Port (AGP) bus, which is capable of much faster data transfer rates than PCI.
PCI-X was developed by industry giants IBM, Hewlett-Packard and Compaq in 1998. It differs from PCI in that it is faster - current 32-bit PCI buses, operating at 66 MHz, can transfer up to 266 Mbytes / second - 64-bit PCI, also running at 66 MHz, can get that figure up to 532 Mbytes / second. PCI-X is a 64-bit bus running at 133 MHz, providing a maximum burst data exchange rate of 1.06 GBytes / second.
Bandwidth is not, however, the entire difference. PCI-X is much more fault tolerant than ordinary PCI. While a failing PCI card can bring a whole system to a grinding halt, PCI-X can reinitialize or terminate a faulty card before failure occurs. PCI-X systems can use PCI cards (the physical connectors fit either type of card) but then the bus speed is limited to that of the slowest card, something which can severely limit overall performance.
The main applications of PCI-X are high-bandwidth devices such as Gigabit Ethernet NICs, Fibre Channel, high-speed SCSI and multi-processing systems. PCI-X is an open standard which anyone can use; currently, Compaq is one of the few companies to release network servers which are PCI-X enabled. Compaq also offers PCI-X development tools on their web site. Several corporations have expressed interest in developing PCI-X peripherals.
However, processor maker Intel is already working on a new I/O standard to succeed PCI-X: Arapahoe, or 3GIO as it was formerly called, will take the place of PCI-X by 2003 if Intel gets its way. Not much is known at this point about Arapahoe, see the Arapahoe node for more information. Also, AMD have already presented the world with HyperTransport, another possible replacement for PCI and PCI-X, with transfer rates up to 12.8 Gbytes / second - more than 10 times what PCI-X can do.
Update (Oct 2003): Arapahoe, aka PCI Express is slowly making inroads, but not on desktop PC's just yet. My above guess that AMD's HT would become another PCI replacement has proven false; instead, it has found its role as a powerful interconnect between various motherboard chips, most notably in the hugely successful nForce and nForce 2 chipsets.
Update (Apr 2004): Someone suggested that PCI-X == PCI Express. Can anyone confirm?