How we cite our quotes: (Paragraph)
Quote #1
Certain persons in the state of Arkansas […] have wilfully obstructed the enforcement of orders of the United States District Court. (2)
The United States District Court had agreed that the law (integration) is valid. Some individuals in Arkansas have decided it's not. Eisenhower's got the subtweet down when he calls out "certain persons" who aren't following the law. He's basically saying, "you know who you are." They made their choice, and he's making his.
Quote #2
Such wilful obstruction of justice […] makes it impracticable to enforce such laws by the ordinary course of judicial proceedings. (3)
Usually, when a law goes into effect, people obey it. That's not happening here, and Eisenhower's had enough. In this line, he emphasizes how destructive this is to the judicial process in general—if people continue to blatantly ignore laws, then the whole system starts to fall apart.
Quote #3
The command contained in that Proclamation [No. 3204] has not been obeyed and wilful obstruction of enforcement of said court orders still exists and threatens to continue. (6)
The lawbreakers were given the opportunity to stop, but they chose not to. It's one thing to choose not to obey a law; it's way worse to actively obstruct it, Faubus's choice is about to bring the hammer down on Little Rock.
Quote #4
The Secretary of Defense is authorized and directed to take all appropriate steps to enforce any orders of the United States District Court for the Eastern District of Arkansas for the removal of obstruction of justice. (9)
Since the courts can't function in their usual capacity (i.e., the law was disregarded), the military will help them out. We're guessing it's a bit easier to say no to a judge than it is to the 101st Airborne. These folks were dispersed by guys with rifles and bayonets, some of whom probably had their own doubts about integration. Unlike the protestors, they chose to follow orders.