Lag is the vector that seperates any 2 locations. Being a vector, the lag has both a distance and direction.
In an effort to uncover a variogram's structure, similar lags are grouped together (i.e., pairs of points aligned in roughly the same direction and roughly the same distance from each other) into bins. Lag size is the width (distance) of the bins into which these vectors are grouped.
For example, if a lag size is set to 10, then the first bin will display (as variogram dots) the average variogram values for all lags = 0 to 10 in length, the second bin will show all those from 10-20 in length, and so on, for the total number of lags (or bins) specified.

See the ESRI documentation "Using ArcGIS Geostatistical Analyst"
pages 28, 31, 64, 66, 73, 171, and 281.

There are no set rules for determining what lag size should be used. It is the craft of the researcher, thier knowledge of the phenomenon they are analyzing, and the reason(s) for modeling a variogram that help to determine the appropriate lag size.
Consider what happens when we take lag size to its extremes. A lag size = 0 will produce a variogram cloud that perfectly displays all possible pairings, but makes interpretation of the variogram structure difficult. At a lag size = infinity (or a distance at least as large as the maximum distance between any two samples), we get one value represented by a single point that represents the average distance and average variogram value for all sample pairings. Selecting an appropriate lag size between thses extremes will allow for the creation of a manageable semivariogram to aid in interpretation.

In most cases you would like to have as many pairs of points as possible represented in any one variogram point. The more pairs a variogram point contains, the more it is of the sample values overall. More pairs per variogram point, however, means a wider bin, and a wider lag distance typically results in less structure for the first points in a variogram.

There are 2 rules of thumb for selecting a lag size:
(1)Have at least 30-50 pairs minimum for any one variogram point. Smaller bins or lag size means less pairs and probably better structure, but too small a bin or lag size typically introduces more noise into the variogram.
(2)Multiply the lag size by the number of lags, which should be about half the largest distance among all points.

A semivariogram, covariance, or cross-covariance cloud depicts all possible pairs of points for a range of lag distances. The default dataset of 300 points totals nearly 45,000 point pairs, and even these can be difficult to display and interpret.

Datasets with hundreds or thousands of samples should be restricted to smaller domains, to avoid overcrowding the variogram/covariance cloud diagram.
Geostatistical Analyst default values can be changed using the ArcMap Advanced Settings Utility.

For ArcGIS, versions up to ArcGIS 8.1 run AdvAMSet.exe located in the ArcObjects Developer Kit\Utilities\VBAdvancedSettingsUtility.

For versions 8.1.2 and above, run AdvancedArcMapSettings.exe located in %ARCHOME%\Utilities.

The six types of Kriging methods used in Geostatistical Analyst are:

Ordinary
Simple
Universal
Indicator
Probability
Disjunctive

Ordinary kriging. This method produces interpolation values by relying on an unknown mean value, allowing local influences due to nearby neighboring values. When the mean is unknown, there are few assumptions. This makes ordinary kriging particularly flexible, but potentially less powerful than other methods.

Yes. Block interpolation is available for all interpolation methods, including deterministic, when the results of prediction are exported to a raster format. The grid option in the symbology tab of the property dialog for a geostatistical layer allows the display of the results of prediction using block interpolation.

The kriging interpolation method is usually associated with exact interpolation. When semivariogram and covariance models have a nugget effect there is potential for a discontinuity in the predicted surface at the sample data locations. Kriging predictions change gradually and relatively smoothly in space until they get to a location where data has been collected, at which point there is a "jump" in the prediction to the exact value that was initially measured.

Variations of kriging can produce noise-free predictions. For example, the filtered kriging interpolator produces a map that is smooth and free of "jumps" at the sample data locations. Consequently, the prediction standard errors are smaller because the nugget component of variance, which is probably due to measurement error, is not predicted. The algorithms incorporated in Geostatistical Analyst can provide exact filtered value predictions at sample data locations. This prevents discontinuities in predictions and the associated standard errors, yet retains standard errors that are comparable to those for exact kriging.

No. The current version of the Geostatistical Analyst does not support barriers or breaks in the semivariogram or covariance. Barriers can be used with the Spatial Analyst Extension using the Inverse Distance Weighted (IDW) interpolator to represent cliffs, ridges, islands, or other breaks in a landscape.

Yes. Geostatistical Analyst is an extension for the ArcView, ArcEditor and ArcInfo Desktop products. It does not work outside of the ArcGIS Desktop software environment.

The value at an unknown location is predicted using only those data points located within the search neighborhood when it has been defined. Point locations are only assumed for those points within the defined search neighborhood. When using a small neighborhood, a trend component in the data can be ignored. As a guide, select the number of neighbors on the basis that few will have a prediction weight of less than 1%.

Yes. Exploratory Spatial Data Analysis (ESDA) tools can be used to detect both global and local outliers. Tools are also embedded into the Geostatistical Wizards to identify erroneous data; for example, variography, detrending, validation and cross-validation dialog boxes.

The range of values in the grid is based on the values stored in the grid. The default minimum and maximum values displayed for the Geostatistical Analyst layer are obtained from the sample data used to create the surface. These values are considered threshold values for the Geostatistical Analyst layer.

A Geostatistical Analyst layer can be displayed to only show those areas that are within the default range of threshold values.

1. Right click the Geostatistical Analyst layer and select Properties.
2. Select the Symbology tab.
3. Select the Show option to be modified.
4. Click the Classify button.
5. Uncheck the Data Exclusion Lower and Upper Threshold options.
6. Click OK on the Classification dialog.
7. Click OK on the Layer Properties dialog.

The classification of a Geostatistical Analyst layer can be modified to display values outside of the default range of threshold values.

1. Right-click the Geostatistical Analyst layer and select Properties.
2. Select the Symbology tab.
3. Select the Show option to be modified.
4. Click the Classify button.
5. Set the Classification Method to Manual or Equal Interval.
6. Check the check box for Custom Min & Max.
7. Modify the Min or Max values in the list of Break values.
8. Click OK on the Classification dialog box.
9. Click OK on the Layer Properties dialog box.

Unlike cross-covariance, the cross-semivariogram can only be used for coincidental data locations. Additionally, the cross-semivariogram is limited because it cannot be used to estimate the shift between variables.