Contrasts can be created in different ways. For example, a combination of a natural and a very engineered figure can constitute a contrast - or the combination of a very big and a small element. These two examples are not applicable to logo design without fail, but the following examples are:

Contrasts develop when coloured elements are mixed with black-and-white elements. This can be considered for logo design, but you should always keep in mind that the logo may be used just in black-and-white in some cases (e.g. for faxes). In those cases, the effect of this contrast - and possibly the effect of the whole logo - may be lost.

In logo design, line thickness - or the combination of thin elements with thick elements - is a very good way of creating contrasts. If they are wisely used, they result in a good outcome in conjunction with proper spatial partitioning.

In this image, the small lefthand squares seem brighter, and the right ones seem darker than they are actually. The eye is deceived by this figure.