DACA happened because the GOP filibustered the Dream Act legislation, and Obama, having compassion, made the considered and informed decision to implement an enforcement policy that shows grace to a category of illegal immigrants who are productive, non-criminal members of our society, voluntarily self-identifying as illegals, and who were initially brought here as children, not by their own volition.
DACA hasn't been ruled on by the Supreme Court -- Trump doesn't get to decide what's constitutional or not. that would be a power grab in its own right, acting as though that the Executive branch gets to do the Judicial branch's job. it's premature for anyone to call it 'unconsitutional' and it has in fact passed challenges in lower courts many times.
DACA is an enforcement policy: the Executive branch has the responsibility to enforce the laws, and it is within its prerogative to prioritize enforcement of law when it is not possible to fully enforce it for all cases. DACA is a guiding principal of enforcement that amounts to neglecting to pursue deportation for people brought to the US as children so long as they are not engaged in criminal activity, apply for consideration for deferred deportation, and remain registered in this way under the act. inasmuch as this prosecutorial discretion, it is not unconstitutional and not an illegal power-grab, and it is not without precedent.
it's the same thing, fundamentally, as police in your town deciding not to pull everyone over and write them tickets for going 1mph over the limit: while technically they have every right to do so, because there are pragmatic limits to how many people who are breaking motor vehicle laws can reasonably be apprehended and prosecuted, the police force pragmatically and preferentially makes the decision to concentrate their efforts on what it deems as more serious and dangerous crimes.