There are several purposes. One is to pray for one another. St. Optatus describes this purpose in a book against Donatism: “Christ, foreseeing this time----how it would come to pass that you should today be at variance with us, gave such commands with regard to prayer, that, at least in prayer, unity might remain, and that supplications might join those who should be torn asunder by faction. We pray for you, for we wish to do so, and you pray for us, even though you do not wish it.” (Against the Donatists Book 4 Chapter 2)
Another purpose is to help us be friendly with one another. This goes a long way. Enemies are hard to convert. Friends are easier. St. Peter Faber said: “[We should] win their goodwill and inclinations to such an extent that they may reciprocate our kind feelings and think well of us. This may easily be done by speaking to them affectionately, and dwelling in familiar conversations on those points only on which they agree with us, avoiding everything like a dispute, in which one side always assumes an air of superiority, and shows contempt of the other. Those subjects should be first chosen in which there is a sympathy and union of wills, rather than those which tend to disunite them by opposition of opinion.” (Instructions How to Deal with Heretics, as it appears in The Life of Blessed Peter Favre by Giuseppe Boero, Chapter 13)
Another purpose is to be a good example of charity to others. Pope St. Gregory VII says: “We and you must show in a special way to the other nations an example of this charity, for we believe and confess one God, although in different ways, and praise and worship Him daily as the creator of all ages and the ruler of this world.” (Letter to Anzir [Nacir], King of Mauretania)
Thus ecumenism seems to have at least three purposes: it helps Catholics and non-Catholics pray for one another, it helps us be friendly toward one another, and it helps us be good examples to unbelievers. All of these have the goal of full conversion to God’s will and then full unity.
Why does the Church pursue this policy of trying to consolidate unity between Christian churches if we confess that the Catholic Church holds the Fullness of the Truth?
One reason is because the two goals are not incompatible, but lead to one another. Vatican 2’s Decree on Ecumenism notes that the Catholic Church is “the one Body of Christ into which all those should be fully incorporated who belong in any way to the People of God.” (Unitatis Redintegratio 3) Ecumenism thus helps bring all people into the fullness of truth in the Catholic Church. Ecumenism would be incomplete if it didn’t have a goal of helping people find the fullness of the truth.
Finally, what significance should ecumenism hold for a Catholic and would it be wise or foolish to disregard ecumenism altogether?
It would not be wise to disregard ecumenism. We can’t give up on what the Church Fathers and Doctors and Ecumenical Councils have bequeathed us, and ecumenism is one of those things. Ecumenism helps people be at prayer for each other, more friendly toward one another, better examples to unbelievers, and contributes toward conversion to the faith. Because of those good things, and probably several others which aren’t coming to mind right away, we can’t disregard ecumenism.