Downtown Disney is a shopping, entertainment and dining 'district' that is part of the Disneyland Resort. Think of it as a nicer outdoor mall. One end of DTD is at the security/bag check before you head into the parks and the other end is the Disneyland hotel.
DTD does not require park admission. There is a range of restaurants and snack shops as well as Disney and non-Disney stores (ie- Sephora). One of the two monorail stops is in DTD on the DLH end (other stop is in Tomorrowland).
When someone says Disneyland (DL), they are referencing Disneyland Park.
The Disneyland Resort (DLR) is a reference to the area encompassing both parks (Disneyland Park and Disney California Adventure), the Downtown Disney District, and the 3 official onsite hotels.
Downtown Disney, like mentioned above, is a shopping district with a bunch of shops and restaurants. Unlike the 2 parks, you do not have to pay admission to DTD. It makes for a great break from the parks or a classic "first evening before the parks" activity.