Cede means to surrender possession of. The main definitions of concede are (1) to acknowledge something as true or correct, (2) to admit defeat, and (3) to yield or allow something. These words have been mixed up for so long that some dictionaries have given up and assigned them one another’s definitions. They’re usually kept separate in edited writing, though, and there’s no reason careful writers shouldn’t also honor the distinction between these useful words.
Cede is also occasionally confused with secede, which means to withdraw formally from membership in an organization.
These writers use cede in the conventional sense:
On Monday he gave a speech suggesting that he was prepared to cede most of the West Bank to a Palestinian state. [Washington Post]
While the original chapel was ceded to English Presbyterians in the 17th century, two small dwellings opposite were converted into a secret chapel. [Telegraph]
A NSW Department of Education spokesman denies that this ceding of responsibility has gone too far. [Sydney Morning Herald]
And these writers use concede in its conventional sense:
There is, most Conservatives will even concede, a limited role for public financing of political parties. [Toronto Sun]
Late in the day, Ms. Fujimori conceded the election and said the country should seek to heal the rifts from a polarizing campaign. [Wall Street Journal]
Amir took four wickets in seven overs, conceding just nine runs. [Irish Times]