What kinds of cases are handled by federal district courts, and in what kinds of cases do united states courts of appeals have
jurisdiction? (site 1)

The  federal district courts handle only hear cases in which US is a party, cases evolving violation of constitution or 'federal law', crimes on 'federal land bankruptcy' cases.  The US court of appeal decides appeals from any of the district courts that are in federal judicial circuit. The appeals court also can hear 'appeals' from some 'administrative agencies' .

Explanation:

Federal court can also 'hear cases' based on the state law which include parties from various states while federal court handle fewer cases. The district court have 'jurisdiction' to hear all parts of Federal cases which includes both criminal and civil cases. A court of appeal hears challenge to district court decision from courts  present within its 'circuit' as well as appeal from decision of 'federal administrative agencies'.