The practice of etikaf, or spiritual retreat, practiced in the last days of Ramadan is symbolic etikaf. The real etikaf is meant to be performed throughout the month of Ramadan. 
This real etikaf is intellectual etikaf.  A believer is required to go into etikaf for a few days. But the real etikaf is intellectual etikaf, which is to be continued throughout Ramadan. 
What is intellectual etikaf?
We live in this world and have many activities in which we engage ourselves. Every moment, we are involved in some or the other activity, or in fulfilling some necessity. We are continuously involved in our family or society, in one form or another. Then what is etikaf? Etikaf is to focus your mind on God in the midst of all activities. In other words, humans represent a kind of dualism. That is, he must have his focus solely on God, while being in the midst of various activities. The dualism is that a person should be focused on God, even though he is engaged in the activities of the world. This means that one does not have to go into seclusion. Ramadan does not mean going into seclusion. Rather, Ramadan is about intellectual etikaf -- going into retreat as far as the intellectual side of your personality is concerned. 
For example, if the lid of my mug falls on the ground, then that is a material event. But I discovered the glory of God through this observation. I realized I cannot even control the lid of a mug in my hand. God, however, is so powerful that He controls the entire universe. 
This is an example of practicing intellectual etikaf in the midst of the diverse activities of the world. 

Your practical or physical side will remain involved in various activities. You cannot change this situation. Even if you go on a mountain top, you will still have to be part of some material activities. You cannot become inactive even there. Etikaf is to focus on God and the Hereafter in the midst of the diverse activities of the world. So, a person has to develop a focused mind. He will continue to be involved in different activities. This can never be changed, even if he were to retire to a jungle. You will be involved in various kinds of different activities. But your mind should be focused solely on God. 
The purpose of Ramadan is to train you in the practice of intellectual etikaf. We must learn to lead a life of intellectual etikaf. This is not only required in Ramadan. In this month we are trained to observe etikaf. In the last ten days of Ramadan, we are trained in this practice with greater intensity. In this period, we are required to retreat to a mosque. But the real purpose is not to simply go and sit inside the mosque. 
The real significance of etikaf is to detach yourself intellectually, or to develop the art of detached thinking. That is, to remain in the midst of all activities but think separately from these activities.