Throughout the first two chapters, we learn that we have a pretty big internal problem. This problem is about how we have done some not-so-good things in the past and is known as "sin". When writing about the sin problem, Paul noted some psalms that talk about how none of us are righteous. Then Paul brought some more psalms to show the sad state of humanity as a whole (granted, some people don't do these things, but unfortunately, many people do such things, and none of us is completely righteous).
Paul talks about how for many people the "throat is an open tomb" and how people "have practiced deceit" (3:13). The quote is from Psalm 5:9, where David is stressed from the many enemies he encountered. Paul even talked about how "poison of asps is under their lips" (3:13), a quote from Psalm 140:3 that is also about David getting stressed from evildoers. Long story short, lies ruin lives.
In addition to various lies from the mouth, Paul also talks about how for many people the "mouth is full of cursing and bitterness" (3:14). It's from Psalm 10:7, another psalm from someone stressed by evil. People not only lie but also throw down others with words, which ruin others' lives.
Paul then talked about how for many people the "feet are swift to shed blood", how many ways involve "destruction and misery", and how "the way of peace they have not known" (3:15-17). The quotes are from Isaiah 59:7-8, where Isaiah is describing the Israelites after disobeying and disregarding God multiple times. While the passage is directed towards the Israelites, the themes of how sin is destructive still apply in the present way. It's also why showing the way of peace is important.
Paul finishes off by talking about how "there is no fear of God before their eyes" (3:18). The section is from Psalm 36:1, where David described the wicked. Even today, many people who do evil show no regard for what is good.