dygraphs per-series and per-axis options
When you create a Dygraph object, your code looks something like this:
  g = new Dygraph(document.getElementById("div"),
                  data,
                  { options });
This document is about some of the values you can put in the options parameter.
per-series options
Typically, an option applies to the whole chart: if you set the strokeWidth option, it will apply to all data-series equally:
  g = new Dygraph(document.getElementById("div"),
                  "X,Y1,Y2,Y3\n" +
                  "1,2,3,4\n" +
                  ...,
                  {
                    strokeWidth: 5
                  });
Some options, however, can be applied on a per-series or a per-axis basis. For instance, to set three different strokeWidths, you could write:
  g = new Dygraph(document.getElementById("div"),
                  "X,Y1,Y2,Y3\n" +
                  "1,2,3,4\n" +
                  ...,
                  {
                    strokeWidth: 5,  // default stroke width
                    series: {
                      Y1: {
                        strokeWidth: 3  // Y1 gets a special value.
                      },
                      Y3: {
                        strokeWidth: 1  // so does Y3.
                      }
                    }
                  });
The result of these options is that Y1 will have a strokeWidth of 1, Y2 will have a strokeWidth of 5 and Y3 will have a strokeWidth of 1. You can see a demonstration of this here.
per-axis options
Some options make more sense when applied to an entire axis, rather than to individual series. For instance, the axisLabelFormatter option lets you specify a function for format the labels on axis tick marks for display. You might want one function for the x-axis and another one for the y-axis.
Here's how you can do that:
  g = new Dygraph(document.getElementById("div"),
                  "X,Y1,Y2,Y3\n" +
                  "1,2,3,4\n" +
                  ...,
                  {
                    axes: {
                      x: {
                        axisLabelFormatter: function(x) {
                          return 'x' + x;
                        }
                      },
                      y: {
                        axisLabelFormatter: function(y) {
                          return 'y' + y;
                        }
                      }
                    }
                  });
The keys in the 'axes' option are always 'x', 'y' and, if you have a secondary y-axis, 'y2'. If you set the "axisLabelFormatter" option at the top level, it will apply to all axes.
To see this in practice, check out the two-axes test.