Previously, Jesus talked about how he provides a path to escape from future judgment and to get to eternal life (especially for people like us who know have screwed up). Speaking of which, if you want to see that article, the title is "John 5:24". Now Jesus will talk about what he meant by "judgment".
Once again, Jesus establishes his authority to give life and judgment because of his link to the Father (5:26-27). Now let's talk about the process.
First, all the dead people would be able to hear from Jesus and live (5:25). After the resurrection, those who "done good" would go to the "resurrection of life" and those who "done evil" would go to the "resurrection of condemnation". From the immediate context, the "done good" refers to people who believe in Jesus, as called for in 5:24 (Grace in Focus). As for people who "done evil", they would face condemnation. Condemnation is essentially getting strong disapproval, and in a judiciary setting, it involves being declared guilty (especially with overpowering holy standards factored in). And being guilty is a scenario that's not good to be in.
Finally, in 5:30, Jesus states that the judgment process is righteous because Jesus does not "seek [His] own will but the will of the Father". Even though Jesus directly handles the judgment process, the Father also has some role. Both work together, and considering God's overwhelming knowledge, the judgment would be righteous.
If we're being honest, we have done some not-so-good stuff towards other people, and that would not look good in our report. However, our life does not have to end in a bad ending -- we know we can have the good ending because Jesus provided a way to be cleared. For more information, John 5:24 is a good place to read or review.