Among the various approaches to understanding literary works--formalist, biographical, psychological, gender strategies--the historical approach is one of the oldest. The historical approach to literature simply means that the critic--the person trying to understand any work of literature--looks beyond the literature itself to the broader historical and cultural events that might influence the author whose work is being considered. The critic will begin to research what was going on in the world at the time the literary work was being written in order to see if the author either consciously or unconsciously incorporated outside forces into the literary work.
For example, when we read the Anglo-Saxon poem Beowulf, which was written sometime around 700 to 800 AD, we notice that the poet often refers both to pagan gods and rituals and to Christianity. At times, the poet may refer to the pagan concept of fate, Wyrd, and two lines later refer to the will of God, clearly an intermingling of the Anglo-Saxon's first religion, paganism, with a religion they adopted beginning in about 600 AD, Christianity. To understand this mix of religions in the work of literature, critics try to understand exactly how and when the Anglo-Saxon people were converted from paganism to Christianity, so they look outside the text of Beowulf to see what events led to the transition from paganism to Christianity and, more important for the literary critic, the timing of that transition. Understanding the timing may help literary critics to understand when the poem was composed.
The historical approach, then, usually helps the critic and readers to understand all of the events and forces that might affect the author as he or she is composing the work, and this gives us a more comprehensive understanding to the work itself.