While Jesus talked about how the truth will set people free, some people questioned Jesus's comment. They thought that because they are Abraham's descendants and are not in bondage that they don't need to be freed.
However, Jesus had a different kind of freedom in mind. Rather than the freedom as in not being in bondage to an oppressor, the freedom in Jesus's mind is freedom from our screw-ups known as "sin". Additionally, from 8:35, Jesus talks about how slaves don't have to be slaves forever, but sons get to be sons forever. Paul further elaborates on how Jesus turned us from slaves of sin to sons/daughters of God in Romans.
Thus, Jesus proclaims that "if the Son makes you free, you shall be free indeed" (8:36). Jesus provides us a way to be free from our past screw-ups via faith in Jesus; once we receive it, we are guaranteed to be free from our past screw-ups.