What were the succession rules?

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http://en.wikipedia.org/wiki/History_of_the_British_line_of_succession #Edward_VI
Edward VI left a Devise for the Succession which he had no authority to do, unlike his father (Henry VIII), to whom Parliament had granted such authority.

http://en.wikipedia.org/wiki/Third_Succession_Act
The Treason Act 1547 made it high treason to interrupt the line of succession to the throne established by the Act of Succession. Edward VI meant to bypass this Act in his "Devise for the Succession", issued as letters patent on 21 June 1553, by naming Lady Jane Grey as his successor in place of Mary. Prevailing over Lady Jane Grey, Mary ascended the throne per the terms of the Third Succession Act.

In addition to the comments above, remember that Edward was a minor when he made his will.

Parliament ruled the succession, not kings. Henry VIII's will was an exception, and one approved by Parliament. Edward's Devise for the Succession never went through Parliament.

But John Dudley's ambitions aside, consider what Henry VIII went through them get a male heir. It was not accepted generally that a Queen Regnant could succeed. Unfortunately there was a considerable dearth of male heirs at the time. Henry's daughters were unmarried and of questionable legitimacy. Henry 2 sisters were his only siblings who had heirs, and all of the surviving ones were female: Mary Queen of Scots if you discount the idea that Henry's sister Margaret gave up her place in the English succession when she married James IV; or if you follow Mary Tudor Brandon's line you end up with Frances Brandon Grey, who also had no make heirs.

Edward's Devise, if you look at the original, actually leaves the throne to Jane Grey's heirs male. But with Edward sinking fast and Jane married only a month when Edward VI died, the phrase was crossed out and replaced with Jane Grey herself and her heirs male. Whatever Dudley's plan, Edward was seeking to entail the crown to the next Tudor male heir.

It has always been said that Henry left Frances Brandon Grey out of the Succession for unknown reasons, but I remember Eric Ives had a discussion about this in his biography of Lady Jane Grey. Unfortunately, my Kindle died before I could get further into this bio and I haven't been able to finish it yet. But Ives is worth listening to.

Mary was the only child of Henry VIII and Queen Catherine to survive childhood.

Elizabeth was the only child of Henry VIII and Queen Anne.

Edward VI was the only child of Henry VIII and Queen Jane.

Edward was the only male heir which made him heir to the throne, he died childless.

Mary was the older daughter so she was next in line when Edward died. She died childless. Elizabeth was next in line after Mary.

Jane Grey was a cousin to the Royal children with no claim to the throne under the laws of succession. By law she was a usurper. At that time the penalty for usurping the throne was death.