The relevant passages
Jesus claims to be God and is confronted by the Pharisees.
The Jewish leaders replied, “We are not going to stone you for a good deed but for blasphemy, because you, a man, are claiming to be God.” Jesus answered, “Is it not written in your law, ‘I said, you are gods’? If those people to whom the word of God came were called ‘gods’ (and the scripture cannot be broken), do you say about the one whom the Father set apart and sent into the world, ‘You are blaspheming,’ because I said, ‘I am the Son of God’? If I do not perform the deeds of my Father, do not believe me. But if I do them, even if you do not believe me, believe the deeds, so that you may come to know and understand that I am in the Father and the Father is in me.” Then they attempted again to seize him, but he escaped their clutches.John 10:33–39, NET
Now that Scripture which Jesus quotes is Psalm 82:6.
God presides in the great assembly; he renders judgment among the “gods”: 2“How long will you defend the unjust and show partiality to the wicked?... 6“I said, ‘You are “gods”; you are all sons of the Most High.’ 7But you will die like mere mortals; you will fall like every other ruler.” 8Rise up, O God, judge the earth, for all the nations are your inheritance.Psalm 82:1–8, NIV
And in the NET, which takes "the assembly of El" as a reference to the Canaanite high god El:
God stands in the assembly of El; in the midst of the gods he renders judgment. 2He says, “How long will you make unjust legal decisions and show favoritism to the wicked? ...6I thought, ‘You are gods; all of you are sons of the Most High.’ 7Yet you will die like mortals; you will fall like all the other rulers.” 8Rise up, O God, and execute judgment on the earth! For you own all the nations.Psalm 82:1–8, NET
The meaning
Who are these gods?
Now the NET version believes the assembly is of the Canaanite god "El", and so this is judgment against their gods for failing to uphold justice. The NIV renders it differently, making it the great assembly of heaven, thundering judgment against the rulers of the land who are called 'gods'. Perhaps they are called 'gods' in quotes because they fancied themselves that title but are doing such a dismal job of it, or because as rulers, they are God's representatives.
In no way is this saying that all people are literal gods. It's talking about a small group of rulers, or, a group of demons. Like Mike Winger notes, if we go with the NIV translation, these people are not gods as their identity, but rather, gods as their authority. They are acting on God's behalf, making judgments as rulers. Thus, the judge of all the earth is testing their judgments and is not impressed.Mike Winger, How New Age & Word of Faith Misunderstand the Bible (Mike Winger and Melissa Dougherty), 1/Sep/2019, https://www.youtube.com/watch?v=d3NVJU82du8
Furthermore, it's judgment against them. It's making a mockery of what they say about themselves. You are gods?! But you can't create justice in the land (v2). You oppress the poor (v3-4). No—you will die like the mortals you are, like all the other rulers (v7). It's a corrective against people who say this—and that's why there's only one example of it in Scripture.
What is Jesus saying?
Now, Jesus is trying to say that the Pharisees should judge him by his actions. While the group talked about in Psalm 82 was shown to lack justice and care for the poor, Jesus is saying that we can know if someone is truly a god if their actions line up with what is expected of God (look at my deeds—John 10:25, 32, 37-38). Given that he was doing good everywhere he went, restoring justice and caring for the poor and needy, he expected the Pharisees to be able to judge that he was indeed God.
(Winger believes what Jesus is saying is a contrast: if this can be said of humans—if you want to call rulers God's representatives—how much more the Messiah, who is God in the flesh. It's not a comparison but a contrast.)
Further correctives
The only group of beings that seek to elevate themselves to the status of godhood are the Devil and his angels.
This was the first lie: "you shall become like God" (Genesis 3:5). This was his heart:
You said in your heart, “I will ascend to the heavens; I will raise my throne above the stars of God; I will sit enthroned on the mount of assembly, on the utmost heights of Mount Zaphon. I will ascend above the tops of the clouds; I will make myself like the Most High.”Isaiah 14:13–14, NIV
But God replies:
But you are brought down to the realm of the dead, to the depths of the pit.Isaiah 14:15, NIV
In great contrast, we are continually called, in every area of our lives, to humble ourselves under God; to take up our cross; to love God and love others—putting their needs before ours; to have less of us and more of God; to know that it is more blessed to be meek, for they will inherit the earth.
So when the Bible screams over and over that we are less than God, on hearing a doctrine that instead elevates us to God's place, we ought to be very wary. This is particularly the case when trying to make a doctrine out of one verse, and one as complex as this.
Implications
Since we're not gods, we need him! We must take up our cross daily, because it's not about our will—which is powerless—but life is about doing God's will. And God has all the power.
Since we're not gods, we can't create things out of thin air, as Scripture says—only God can create (John 1:3; Colossians 1:16).
Since we're not gods, we only have delegated power. We are ambassadors, so that if we go beyond what God has said, we overstep our authority. Overstepping our authority is a serious issue, and is sometimes called presumption. So we have power to do what God wants to do in one situation, but cannot do the same thing in another situation without his power and authority for that too. Each situation requires God's approval (see the Directionalism series).
Rather than teaching that we can direct God, we need to be on our knees looking to what God wants to do through us.