If you want to read the article by Darrell Whiteman, you can click HERE. But grabbing some excerpts, the first  purpose is as follows

Contextualization attempts to communicate the Gospel in word and deed and to establish the church in ways that make sense to people within their local cultural context, presenting Christianity in such a way that it meets people’s deepest needs and penetrates their worldview, thus allowing them to follow Christ and remain within their own culture.

This function seems at first to be self-evident, but it is clear we have not always done mission in this mode. Why, then, this sudden burst of energy and excitement, at least in the academy, about this notion of contextualization? I believe the answer lies partly in the postcolonial discovery that much of our understanding and practice of faith has been shaped by our own culture and context, and yet we often assumed that our culturally conditioned interpretation of the Gospel was the Gospel. We are now beginning to realize that we have often confused the two and have inadvertently equated our culturally conditioned versions of the Gospel with the kingdom of God.

Now the second function

Another function of contextualization in mission is to offend—but only for the right reasons, not the wrong ones. Good contextualization offends people for the right reasons. Bad contextualization, or the lack of it altogether, offends them for the wrong reasons. When the Gospel is presented in word and deed, and the fellowship of believers we call the church is organized along appropriate cultural patterns, then people will more likely be confronted with the offense of the Gospel, exposing their own sinfulness and the tendency toward evil, oppressive structures and behavior patterns within their culture.   …

Unfortunately, when Christianity is not contextualized or is contextualized poorly, then people are culturally offended, turned off to inquiring more about who Jesus is, or view missionaries and their small band of converts with suspicion as cultural misfits and aliens. When people are offended for the wrong reason, the garment of Christianity gets stamped with the label “Made in America and Proud of It,” and so it is easily dismissed as a “foreign religion” and hence irrelevant to their culture.  When this happens, potential converts never experience the offense of the Gospel because they have first encountered the cultural offense of the missionary or Westernized Christians.

Ant the third function:

A third function of contextualization in mission is to develop contextualized expressions of the Gospel so that the Gospel itself will understood in ways the universal church has neither experienced nor understood before, thus expanding our understanding of the kingdom of God. In this sense contextualization is a form of mission in reverse, where we will learn from other cultures how to be more Christian in our own context.

This is an important function of contextualization in mission because it connects the particular with the universal. The challenge is creating a community that is both Christian and true to its own cultural heritage. Peter Schineller points out in addition that “every local Christian community must maintain its link with other communities in the present around the world, and with communities of the past, through an understanding of Christian tradition.”