There are a few hardware specifications that are absolutely vital when you shop for a motherboard.
CPU Socket Type: This is the type of CPU the motherboard supports. You will probably choose your CPU before your motherboard, so make sure these match.
CPU Type: This is also important in making sure your CPU is compatible. Most likely, if the socket type is compatible this will be compatible as well. But double check!
Number of Memory Slots: This is usually 2 or 4. This is the number of RAM chips you can install.

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Number of Pins: This is the number of pins supported in the RAM slots. If you buy the wrong RAM, it will not fit in the motherboard.
Memory Standard: This is just as important as the number of pins. An example of a memory standard is "DDR2". You need to buy RAM that matches this.
Expansion Slots: Pay especially close attention to the number of PCI Express 2.0 x16 slots (most high end graphics cards require at least a PCI Express 1.0 x16), regular or x1 PCI Express Slots, and plain PCI Slots. You need to make sure you have enough of the right types of slots for any cards you plan to add: graphics cards, sound cards, video capture cards, etc. Differences between PCI, PCI-E and x16 lanes slots are explained here.
Storage Devices: At the time of this article, you will most likely buy a SATA hard drive. So make sure your motherboard supports SATA storage devices.
Physical Spec: Most desktop builders are looking for ATX form factor, available in three sizes; Extended, normal, and Micro. You can put a smaller ATX board in a larger ATX case (e.g.: Micro board in normal case or normal board in E-ATX), but obviously not the opposite. If you have a specific case in mind that is not ATX, make sure it matches with the physical spec for this motherboard.