Donald Trump spent years trying to prove that President Obama was actually born in Kenya and not in Hawaii. President Obama finally produced a birth certificate for Hawaii which had many questions associated with it.
What was the issue? The issue was that the Constitution requires that a President be a "natural-born citizen of the United States." If Obama had been born in Kenya, there would then be a potential question as to whether he satisfied that requirement.
Donald Trump is now raising the same question for Ted Cruz. Cruz was born in Canada to an American born mother and a father who was Cuban. Trump is challenging Cruz to go to court to establish whether Cruz satisfies the "natural-born citizen" requirement.
What are people saying? Senator John McCain agrees with Trump and says he thinks Cruz should go to court -- the Supreme Court. The risk is that, if Cruz gets the Republican nomination, Democrats could challenge him in court just before the election.
The definition of "natural-born" is unclear. If it means to an American father and mother born in America, it is clear. If it means to an American mother and a Cuban father born in Canada, it is not 100% clear. Whether Ted Cruz addresses this issue now or in the future, it will likely not go away.