When manually specifying a bin size for a lidar operation, the bin size you want to set is based on the resolution of your Lidar data. Ideally, you will be able to confirm the resolution of the lidar data from the data source. However, this may also be confirmed or determined in the application by using the Measure tool to measure the distance between points. Typically, just using the automatic bin size setting in the lidar operation will create a bin size based on the detected spacing/resolution of the loaded or selected lidar data.
In Global Mapper, binning lays a regular grid over the point cloud within the defined boundaries of the operation (layer extent unless you have specified otherwise). When you set a bin size, you are telling the application the size that each rectangle in the gird should be. Make the bins at least 2-3 point spacings apart to reduce/eliminate the spikes or troughs where just a single point is in a bin. In the auto-classification tools, this is automated and based on the spacing of the points.
Some more advanced users may choose to over ride the automatic setting and change the bin size, users of all levels can test running auto-classification routines or operations with manual bin size settings to determine appropriate settings for the desired outcome.