HubSpacing, Dropout Width, "Over Locknut Dimension (O.L.D.)".
Importance: The HubSpacing of your new wheel must buy a wheel that matches your frame. Most common is 100mm for front and 135 for rear. The hub spacing usually implies a certain axle thickness, so you don't need to worry about axle thickness.
Definition: This is the distance between the two arms of the frame to contain the wheel hub. The axle itself will be a bit longer and either slips into the slot, or threads into the frame. The "Over Locknut Dimension" O.L.D.) width of your wheel axle should match the dropout width of your frame. For rear wheels, the most standard is 135mm which is currently used on most hybrid and mountain bikes. If you tried to fit an old wheel made for 126 mm dropouts into a 135 mm frame, you'd need 9 mm of spacers. For front wheels, the standard dropout width is 100mm.