Washington is partitioned into quadrants, designated NW, NE, SW, and SE, oriented with respect to the Capitol, which is a mile or so east of the center of the (former) diamond. NW is the largest quadrant, NE and SE are somewhat smaller, and SW is not very large at all (because Virginia took most of it away).
In general north/south streets have number names ( "1st street") with one sequence ascending to the east of the Capitol and another to the west, qualified by quadrant: "3rd street SE" and "3rd street SW" are parallel and change names to "3rd street NE" and "3rd street NW" as they change quadrants to NE and NW (as they pass the Capitol). The White House is at 16th street NW, and there is a parallel street (roughly) 32 blocks away, 16th street SE, whose name changes to 16th street NE when it crosses to the NE quadrant. East/west streets have alphabetic names, some a single letter, e.g. "A Street NE" and some real names: states, like "Alabama Avenue SW" (actually every state in the union is represented), as well as flowers (e.g. "Dahlia"), institutions (" Peabody"), and mysterious entities ( "Quackenbos"). Streets generally change quadrant designation, but not name, as they change quadrants, and there are no parallel east/west streets with the same name. (There are however more exceptions to than instances of these rules, and often a street changes its name from block-to-block for no known reason. Many so-called east/west streets run at sharp angles, radially from the Capitol, and change direction as well as name often.)
On of the biggest barriers to navigation in DC is the disconnected streets. New Hampshire Avenue is the most notorious. Many a naive tourist has tried to follow New Hampshire Avenue from the North to Dupont Circle (a perfectly logical thing to try, since Dupont Circle is formed by the confluence of three major streets, one of them being New Hampshire Avenue). Most of these people are still lost.