The Bible often uses trees and plants as analogies for humans (e.g. Ps. 1:1-3; Jer. 17:7-8). The fruit a tree or plant produces are like the attitudes and behaviour a person produces (e.g. Mat. 7:15-20; Luke 3:8). So, in John 15 Jesus is saying that his disciples should produce attitudes and behaviour in keeping with being a Christian, part of the ‘vine’ (John 15:5).
The “fruit” – the attitude and behaviour – Jesus wants his disciples to produce is summed up in John 15:12, where he says:
This is my commandment, that you love one another as I have loved you.
We should have ‘much’ (John 15:5,8) — lots — of this in our lives.
Gal. 5:22-23 also talks about the “fruit” a Christian should produce:
…the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control…