On the most basic level, a logo is a mark involving either a symbol or typographical mark or a combination of both. A good logo can be reduced to black and white, be only an inch tall, and still be identifiable (this can be a little more difficult with longer business names).
With this being said, a photo is not a part of a logo, ever! A photo can be a part of your overall branding, although it can still be problematic with business cards, letterhead, and envelopes.
So, what is branding? A great example of branding can be seen with Coca-Cola. Their logo is the actual logotype “Coca-Cola,” with that old, gorgeous, “scripty” font. However, there are other elements that are also associated with Coca-Cola in their marketing. The “Coca-Cola Ribbon,” the bottle, and the derivative word “Coke,” are a part of their branding. This is also where color comes in. Color for a logo is also a part of branding (remember: a logo is not a part of branding!). Coke not only has their own formula for red, they also have their own Coke white!
Branding and logo design are directly linked, and necessary to one another. Without a logo, branding is impossible to maintain. One can have a logo without a brand, but there cannot be branding without a logo.