to cause someone trouble or inconvenience; often used when apologizing or expressing gratitude for someone's effort
いつも面倒を掛けてすみません。
I'm sorry for always causing you trouble.
いろいろ面倒を掛けてしまったが、本当にありがとう。
I've caused you a lot of trouble, but thank you very much.
手続きが複雑でご面倒をかけるかもしれませんが、よろしくお願いします。
The procedure is complicated and may cause you trouble, but thank you in advance for your help.