U.S. federal courts are generally organized into district courts, courts of appeals and then the Supreme Court of the United States. The most common federal court that does not fit in this structure is bankruptcy courts, which are below district courts. District courts are the general trial courts of the U.S. federal government. Appeals from bankruptcy court can go to district court or a Bankruptcy Appellate Panel of bankruptcy judges, depending on whether the local federal jurisdiction has set up BAPs. Texas has four federal judicial districts- eastern, northern, southern, and western. I won't go into the boundaries of the districts- they're pretty common-sensical, and you can look them up with the link above.
The courts of appeals for federal district courts are organized into circuits. The Fifth Circuit covers appeals from Texas, Louisiana and Mississippi. Before October 1, 1981, it also included Florida, Georgia and Alabama, but then an Eleventh Circuit was formed for them. It is important to remember if you are citing southern cases from around that time, that Fifth Circuit precedents bind the Eleventh Circuit for cases decided before October 1, 1981. Besides appeals from district courts, the Circuits also hear appeals from some federal agency decisions and from the Board of Immigration Appeals.
Federal jurisdiction is limited. Unless the United States Constitution or a statute allowed by it provides for federal jurisdiction of a matter, the presumption is that federal courts do not have jurisdiction. This contrasts with U.S. state court jurisdiction where there should be some court for nearly any dispute.