An influence plot shows the outlyingness, leverage, and influence of each case.
The plot shows the residual on the vertical axis, leverage on the horizontal axis, and the point size is the square root of Cook's D statistic, a measure of the influence of the point.
Outliers are cases that do not correspond to the model fitted to the bulk of the data. You can identify outliers as those cases with a large residual (usually greater than approximately +/- 2), though not all cases with a large residual are outliers and not all outliers are bad. Some of the most interesting cases may be outliers.
Leverage is the potential for a case to have an influence on the model. You can identify points with high leverage as those furthest to the right. A point with high leverage may not have much influence on the model if it fits the overall model without that case.
Influence combines the leverage and residual of a case to measure how the parameter estimates would change if that case were excluded. Points with a large residual and high leverage have the most influence. They can have an adverse effect on (perturb) the model if they are changed or excluded, making the model less robust. Sometimes a small group of influential points can have an unduly large impact on the fit of the model.