[KyleGoetz]

ていく means "to begin ~ing" or something. I suck at translating it to English, but the point is that something will move towards doing some verb in the future.

中国の人口がだんだん増えていく
China's population will gradually increase

背が高くなったら、バスケをよくやっていく
If I get taller, I will play basketball often