Meaning of “Ocha wo nigosu(お茶を濁す)”

“Ocha wo nigosu(お茶を濁す)” means “Avoiding the subject” or “evasive answer”.

Literally meaning of it is “making a tea muddy”.
“Ocha(お茶)” means tea, “Nigosu(濁す)” means making muddy.
This is a traditional common expression.

Example Conversation

A: By the way, do you have a any relationship?
B: Relationship… well… Oh, can I make a phone call to my client?
A: Go ahead.
— After a phone call —
B: I’m sorry, I have to go now, see you again!!
A: See you. ( Oh, she “Ocha wo nigossita(お茶を濁した)”… )

A: そういえば彼氏いるんだっけ？
B: 彼氏ねぇ…、どうだろうねぇ…。あ、ちょっと電話していい？
A: どうぞー。
電話後
B: ごめん、もういかなきゃ！またね！
A: またねー。（あ、お茶濁された…）