The Connector block allows you to create a malleable bridge for the Storyline, allowing you to visually arrange the graph as you wish.
You can create a connector block by double clicking on a connection to split it in two.
It does not affect the variables or the visualization of the experiment, but it certainly improve the clearness of your project. Indeed, it can sum up a lot of connexions in order to reduce the saturation of your graphic. Also, one can mention its colors, which brightens connexion's colors and help to see different levels of links.
Here is an example of a "normal" graphic without connectors, and another one with connectors. For this reason, connectors are very useful when you want to realize a big project with a lot of crossed connexions.