Speed Class is a minimum speed based on a worst case scenario test. The Speed Class is important for video mode or camcorders, where the device is actually saving a steady stream of data. The resolution and format of the video determines the amount of steady stream data. This translates to a minimum speed you need to guarantee that the video captured on the cards is recorded at an even, sustained rate with no dropped frames (which would result in lost data and choppy playback).
Compared to high-megapixel photography, video doesn't need as big a data pipe because the video format is a smaller "fixed stream" that uses only a portion of the data pipe. But you do need a minimum guaranteed speed for the SDHC card that satisfies the requirement of the data stream. Your camera's specifications should state the minimum SDHC Class Rating required.
Using a card without the proper class rating on a more advanced camera, such as a high-definition (HD) camcorder or Digital Single Lens Reflex (DSLR) camera with HD video record settings is likely to result in an error message indicating that video can only be recorded at a lower definition setting.