In Elul, one contemplates the past year, utterly regretting whatever has been undesirable, and resolving to be vigilant in the meticulous observance of the commandments, to be conscientious in one's Torah study and in one's prayers, and to habituate oneself to positive character traits.
The name of the month, "Elul," is an acronym for the Hebrew words which mean, "I am my Beloved's and my Beloved is mine."
"I am my Beloved's" refers to serving G-d through one's own initiative. When a Jew serves G-d through his own initiative, the bond between G-d and the Jew is internalized. "My Beloved is mine" refers to Divine revelation which inspires this bond. Elul represents a month of complete connection, through revelation from Above and service from below.
This concept is also connected to this week's Torah portion, Re'ei, which begins with the words, "See, I am giving before you today." All of the aspects of our service to G-d should be seen and openly revealed, and not just something we hear about. Seeing implies the establishment of a deep and powerful connection.
In a deeper sense, we should use our sight to see not just the physicality of the world, but also the essence of G-d and His handiwork in our surroundings.