加油
jiā yóu
to add oil; to top up with gas; to refuel
to accelerate; to step on the gas; (fig.) to make an extra effort; to cheer sb on
add (加) + oil (油) = fuel up and cheer on
Originally meant literally adding oil to fuel a machine or vehicle. The cheering sense comes from the metaphor of giving someone extra fuel or energy to keep going.
车没油了，我们去加油站加油。
chē méi yóu le, wǒ men qù jiā yóu zhàn jiā yóu.
The car is out of gas, we're going to the gas station to refuel.
比赛的时候，同学们都在为他加油。
bǐ sài de shí hou, tóng xué men dōu zài wèi tā jiā yóu.
During the competition, the classmates were all cheering him on.