Wilderness conjures up Israel in the wilderness as well as Elijah in the wilderness: a place of testing. But "forty" takes us specifically to Israel in the wilderness. The next word, "tempted" recalls Adam and Eve in the garden of Eden, and "tempted by Satan" reminds us of the tempting of Job, especially the first chapters of Job when Satan seeks God's permission to tempt Job.
In these few words (I suggested in my sermon) Mark, whose gospel is a gospel of restoration (healings, deliverances, feedings), tells us that Jesus comes to put things right for broken down humanity.
Jesus in his own person is reliving the history of us by reliving the story of Adam and Eve being tempted, but this time not falling for the temptation. And, Jesus relives Israel's story of of being tested in the wilderness and passes the test. That is, Jesus in his own person begins the restoration of humanity by showing that the story of human life can be different. The new Adam obeys God and resists Satan. The new Israel demonstrates understanding of the identity and mission God gives to Israel, to bear witness to the one true and life-giving God.
Jesus is also like Job: he has utter faith in God, that God will see him through life, no matter what suffering comes his way.
A further sign of restoration of humanity being the critical theme of these verses is the mention of the "wild beasts". Wild beasts normally eat humans and that did not happen here. That phrase, "wild beasts" thus recalls for us prophetic visions of restoration, when the lion lays down with the lamb.
Thus, when in the next verses we find Jesus proclaiming that the time has come and the kingdom is near, the message is effectively that humanity is about to be restored. The challenge of the passage is for us to also be in the business, within family, community and wider world, of contributing to the restoration of humanity to what God intended us to be.