Bahasa Jakarta (literally, Jakarta language) is the language that a lot of people speak in Jakarta. It’s sufficiently similar to Indonesian to be understood by Indonesians but foreign speakers of Indonesian get lost fast because of the different accent and different vocabulary.
Bahasa Jakarta is closely related to Bahasa Betawi, which refers to the bundle of language traditions (is it a dialect?) spoken by the Betawi people, believed to be the original inhabitants of Jakarta.
As a practical matter, speaking Bahasa Jakarta marks you as a person who has lived in Jakarta. It’s not any harder to learn than anything else, but it’s hard to find people to practice with because it strikes Indonesians as somewhat ridiculous to hear a foreigner speaking in a way that even a Javanese or Sundanese (the two largest ethnic groups in West Java where Jakarta is located) person does not.
Elements of Bahasa Jakarta — especially the accent — are used routinely for sitcoms broadcast on national TV.