Design resolutions describe how much the effects in a fractional factorial design are aliased with other effects. When you do a fractional factorial design, one or more of the effects are confounded, meaning they cannot be estimated separately from each other. Usually, you want to use a fractional factorial design with the highest possible resolution for the amount of fractionation required. For example, it is usually better to choose a design where main effects are confounded with 3-way interactions (Resolution IV) instead of a design where main effects are confounded with 2-way interactions (Resolution III).
Resolution III, IV, and V designs are most common: