One example is the law passed by Congress 21 USC 841 which prohibits production, sale or possession of marijuana: prosecutions have been suspended at the federal level by executive-branch decision, in certain states (Washington, Colorado, others no doubt). Obama indicated at the time that such prosecutions were not high priority, a determination that is uncontroversially within the discretion of any law enforcer. Likewise, the Immigration Accountability Executive Action reprioritized deportations to focus on felons and not children, also focusing on border crossings rather than people in and established.
Congress does not always spell out all of the details, when it passes a law, and may leave some aspects to the executive branch. If the law says "The Secretary of State shall...", then the Secretary of State shall. The degree of compulsoriness would depends on the specific mandate under the law. The law underlying the apolitical nature of 501(c)(3) exemptions is open to some interpretation regarding what it means for a corporation to intervene in a political campaign, thus Congress has implicitly granted the executive branch the power to say what that means, which it has. In 2002 there was a Congressional hearing on this rule, with the report here that includes (starts with) the relevant IRS sub-director testifying as to the IRS's interpretation of the law at the time. The particular prohibited actions that are testified to are not specified by Congress, they are the result of rule-making authorized by 26 USC 501.