When describing faith and works in regards to justification, there's a useful analogy on wages and gifts.
Works are like getting a wage, which are "not counted as grace but as debt" (4:4). The wage system is what makes up most careers today, where we do some tasks to earn some money. The owner/employer has an obligation to pay wages (some areas have minimum wage).
However, for those who "[do] not work but believes on [Jesus]", the faith "is accounted for righteousness" (4:5). As we saw in Romans 3, God initiated the justification plan via the righteousness of Jesus, and keep in mind that none of us were able to match God's standards. Thus, we do not deserve God's righteous provision -- but God did it anyway. So rather than trying to accomplish God's standards (which we can't), we can accept Jesus's righteousness via faith. Hence, Jesus's plan is commonly seen as a gift.
One final note to make regarding beliefs in salvation process. First off, due to how none of us can match God's standards (as seen in Romans 1-3), we can't work for our salvation, so believing only in works does not fly here. As for faith and works, this could get a bit tricky, but note that the Greek word for "work" (Strong 2038) has a sense of "earn by working" and "performing" -- which none of us can accomplish as recorded in Romans 1-3. So mechanically, God's righteousness via Jesus is a gift given by God's grace and not something we earn. We receive Jesus's righteous by believing in Jesus as Lord and Savior (which you can do right now), and mechanically, Jesus is the only reason why we were able to be justified. With that said, good works are still important, but it has a different purpose.