Complete fertilizers (also known as "balanced fertilizers" or simply "NPK fertilizers") are so called because they contain nitrogen, phosphorus and potassium -- the Big 3 in fertilizer ingredients. A fertilizer listed as "10-10-10," for instance, would be a complete one. But one listed as "10-0-10" would not be considered complete, the middle zero indicating the absence of phosphorus in the product. This would be referred to as an "incomplete fertilizer."
Do note, however, that an incomplete fertilizer is not necessarily inferior to a complete fertilizer. Which is better really depends on the circumstances. If your soil already had an excess of one of the three nutrients in NPK, you could actually be harming some of your plants by adding more of it to the soil -- which is precisely what you would be doing (inadvertently) by using a complete fertilizer. This is why it is important to have your soil tested: otherwise, whenever you add anything to your soil, the effect (whether positive or negative) is left to chance.
More info: http://sonefworld.com