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Joyce asked, "Could you tell me what is meant by “things under the earth” in Philippians 2:10?

That passage is referring to a future time when all people will bow before Jesus. Paul is making the point that every knee means literally: every knee. The phrases he uses in the verse are designed to communicate that it is a comprehensive picture of all humanity. 

Here is how we can break it down:

Of those who are in heaven: That includes the holy angels and the redeemed believers of all ages who will have already died before this happens. 

And on earth: That is a reference to all of humanity both redeemed and unredeemed at the end of human history and the great judgment of God. Anyone who is alive at the time when this happens. And then to your specific question:

Those who are under the earth:  That was a common reference to the grave. Paul is referring to all the unredeemed dead who await their final resurrection and judgment. In other words, this refers to all of the unsaved people, and it refers to Satan and all of the demons as well. 

In addition to referring to the grave, the phrase “under the earth” also referred to the underworld or the  “under-earth world.” It is a reference to the demonic kingdom of fallen angels and their leader Satan. They all await their coming and final judgment. All of the demons and the devil himself will one day be compelled to admit that Jesus Christ is indeed victorious.  They will prostrate themselves before the throne of the risen Lord. 

So, the phrase "under the earth" refers to two categories of beings: It refers to everyone who dies without placing faith in Jesus Christ; and it refers to Satan and all of the demons. They will all be included among those who's knees will bow.