Carryover or carry-over refers to insulin effects lasting past the insulin's official duration. It's been observed that some long-acting insulins leave an insulin depot[1] under the skin that has a small residual effect that may last anywhere from 12 to 48 hours, after the principal action has ended.
Keep in mind that any substance injected into the body will be removed or broken down gradually, it won't all disappear at once. So even after there's not enough insulin left to make a noticeable dent in blood glucose, there will still be a period of time when small amounts are present and being slowly used up. In long-acting insulins, those small amounts may give a slight boost to the next day's (or three day's) doses.
This small residual effect, if it exists, may mean that the same dose given 3 days in a row will be slightly more effective each day. For example, Dr. Rand mentions in her Lantus studies[2]: "We have found it often takes 3-5 days for a good glucose-lowering effect to be seen in the glucose curves, possibly because of the long duration of action and carry-over effect of glargine."
For terminology's sake, consider the principal action of the insulin to be its onset, peak, and duration. If you shoot insulin again before the duration has expired, there will be overlap. Carryover is whatever small residual effect is left after duration has expired.