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Below is "regression function" output in ArcGIS Kriging.

enter image description here

I'm assuming the first value is my r2, but does the 2nd value represent error rate, residual, or something else?

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You are correct about value you referredenter image description here to, the residuals:

An excerpt from Esri's Regression analysis basics

Residuals: These are the unexplained portion of the dependent variable, represented in the regression equation as the random error term ε. View an illustration. Known values for the dependent variable are used to build and to calibrate the regression model. Using known values for the dependent variable (y) and known values for all of the explanatory variables (the Xs), the regression tool constructs an equation that will predict those known y-values as well as possible. The predicted values will rarely match the observed values exactly, however. The difference between the observed y-values and the predicted y-values are called the residuals. The magnitude of the residuals from a regression equation is one measure of model fit. Large residuals indicate poor model fit.

I also wanted to add the Residuals Graphics as additional context

enter image description here

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