복잡하다 has two main meanings.
1. complicated, complex, intricate, tangled
일이 복잡하게 됐다
Things have become more complicated.
I have too many things to think about.
2. crowded (with), busy, congested
도로는 휴일 나들이 차량들로 복잡했다
The roads were crowded with holiday traffic.
아침에 지하철은 출근하는 사람들로 복잡하다
During the morning rush hour, the subway gets congested with commuters.