In this context, the bearing of fruit is generalized. It includes everything produced as a result of their labors of publicly preaching the gospel, their service to the church in pastoring, and their personal overcoming and growing in the image of God. They all bring honor to God by declaring the dramatic change for good that takes place as a result of being connected to the Vine and thus able to draw upon Him and His power to produce fruit.
Verse 16 briefly touches on the quality of fruit God desires. It implies that the disciples should be rich in good works and be striving to produce fruit that endures. God wants the fruit to endure both within themselves (by taking on God's character) and in others (in conversions so that the church grows and continues).
The remainder of the verse ties answered prayer directly to the production of fruit. We are all called to participate in the work of the church, if only to pray for it. God has not called everyone to work on the front lines of evangelizing as apostles. But if God has called and chosen us, upon us falls the responsibility of producing fruit within the scope of our place in the body that we all glorify God.