I have been contemplating how to best get across what to look for in a logo for client information, and as luck would have it an excellent post was written on just this subject. Instead of reiterating the entire post, I recommend reading it yourself.
In summary terms, a good effective logo should be 5 things: simple, memorable, timeless, versatile and appropriate. If you look at some of the most famous logos you will see a common theme that includes these five elements (Nike, McDonalds, Coca-Cola, etc.). They seem simple enough to create, however there is much work behind the scenes. Creating a unique brand through use of a logo is an important step for any business to take, this is how your clients will ultimately recognize and remember you - this is what gets imprinted in their memory. A good logo will contribute to your business’s visibility, credibility, and memorability — three factors that will help your business to grow and succeed.
5 Principles of Logo Design