This is actually the net result of the decision - now the people and their legislatures have to make decisions. I'll quote directly from the decision itself:

"The Constitution does not confer a right to abortion; Roe and Casey are overruled; and the authority to regulate abortion is returned to the people and their elected representatives."

What people forget (or never learned in civics class, most likely because their teachers were utterly incompetent) is that the Supreme Court can't just wake up in the morning and decide "You know what? Today, let's write a ruling that says (eg) you have a right to take money from your neighbor if you're destitute."

It doesn't work like that.  A case has to be brought before the court. The law(s) involved in that case, the scope of those laws, along with the cases that came out of lower courts in challenging said law(s) all factor into the case brought before the Supreme Court. Roe v. Wade was litigated with a woman chosen for being destitute and who would go along  with the claims her lawyers made - ie, that she was raped (she wasn't), that thousands of women were dying from illicit abortions (they weren't), that the public supported the agenda of abortion (they didn't - the press helped lie then as now), and so on. No matter, the Roe decision was arrived at by careful venue shopping, picking the correct litigant, carefully choosing the laws to appeal, etc. 

Same thing here. Same thing happened in Heller v. DC.

In this case, Mississippi passed a law that basically outlawed abortion after 15 weeks. Here's the introductory text from the decision, presenting the case:

"The State of Mississippi asks us to uphold the constitutionality of a law that generally prohibits an abortion after the 15th week of pregnancy—several weeks before the point at which a fetus is now regarded as “viable” outside the womb. In defending this law, the State’s primary argument is that we should reconsider and overrule Roe and Casey and once again allow each State to regulate abortion as its citizens wish."

That's it. The Mississippi law was carefully legislated to create the opportunity for this case to go to the Supreme Court. Mississippi might have wanted to more tightly restrict abortion, but they deliberately chose the timeframe of 15 weeks to move the limit into the second trimester. This is important, because Roe was the decision that partitioned pregnancy into trimesters, not by gestational milestones. This was a foolish move by the justices who wrote Roe v. Wade all those years ago...

OK, so with that, how does the Dobbs decision reach the conclusion to overturn Roe v. Wade? Again, it's spelled out for those who take the trouble to read the decision:

"The Constitution makes no reference to abortion, and no such right is implicitly protected by any constitutional provision, including the one on which the defenders of Roe and Casey now chiefly rely—the Due Process Clause of the Fourteenth Amendment. That provision has been held to guarantee some rights that are not mentioned in the Constitution, but any such right must be “deeply rooted in this Nation’s history and tradition” and “implicit in the concept of ordered liberty.” Washington v. Glucksberg, 521 U. S. 702, 721 (1997) (internal quotation marks omitted). The right to abortion does not fall within this category. Until the latter part of the 20th century, such a right was entirely unknown in American law. Indeed, when the Fourteenth Amendment was adopted, three quarters of the States made abortion a crime at all stages of pregnancy. The abortion right is also critically different from any other right that this Court has held to fall within the Fourteenth Amendment’s protection of “liberty.” Roe’s defenders characterize the abortion right as similar to the rights recognized in past decisions involving matters such as intimate sexual relations, contraception, and marriage, but abortion is fundamentally different, as both Roe and Casey acknowledged, because it destroys what those decisions called “fetal life” and what the law now before us describes as an “unborn human being."

The rest is legal inside baseball.

We should note that Ruth Bader Ginsburg said in an interview in 2013 that Roe v. Wade was subject to challenge, because it didn't build a foundation of incremental cases - it cut out the involvement of the state legislatures and the voters and incremental case law. She has been proven correct and prescient.