竞选 (jìngxuǎn) is a verb meaning "to campaign" or "to run for office." It is used in political contexts when someone is seeking election to a position. For example, 竞选总统 means "to campaign for president."
他决定明年竞选市长。
tā juédìng míngnián jìngxuǎn shìzhǎng.
He decided to run for mayor next year.
两位候选人正在激烈地竞选总统。
liǎng wèi hòuxuǎnrén zhèngzài jīliè de jìngxuǎn zǒngtǒng.
The two candidates are fiercely campaigning for president.
她是第一个竞选这个职位的女性。
tā shì dì yī gè jìngxuǎn zhège zhíwèi de nǚxìng.
She was the first woman to run for this position.