Meaning:

Literally “加” means to “add,” and “戏” means “acting.” Originally this term was used to describe actors and actresses who are not leads try to attract attention from the audience by acting dramatically or improvising lines to prolong their screen time. Now, Chinese netizens often use it to refer to scenarios where “drama queens and kings” try to put on a show.

Example:

A: 小明结婚竟然没请他的发小大刘，真让我吃惊。

Xiǎomíng jiéhūn jìngrán méi qǐng tā de fàxiǎo dàliú，zhēn ràng wǒ chījīng。

It surprised me that Xiaoming didn’t invite his childhood friend Daliu to his wedding.

B: 因为大刘幽默风趣，又喜欢给自己加戏，估计小明害怕自己的婚礼上大刘变成焦点了。

Yīnwéi dàliú yōumò fēngqù，yòu xǐhuān gěi zìjǐ jiāxì，gūjì xiǎomíng hàipà zìjǐ de hūnlǐ shàng dàliú biànchéng jiāodiǎn le。

Because Daliu is funny and likes to act dramatically, I guess Xiaoming was afraid that Daliu would steal the show at his wedding.