Recently, I read the paper on Ichino-Ikeda conjecture for unitary groups by Raphaël Beuzart-Plessis (https://arxiv.org/pdf/1602.06538.pdf). In the introduction, it says that
Let $BC(\Pi)$ be the base change of $\Pi$ to $GL_n(\mathbb{A}_E)\times GL_{n+1}(\mathbb{A}_E)$ (known to exist thanks to the recent work of Mok and Kaletha, Minguez, Shin and White).
where $\Pi$ is a cuspidal automorphic representation of $U(n)\times U(n+1)(\mathbb{A}_F)$. $E$ and $F$ are number field, and $E$ is a quadratic extension of $F$.
I am a bit confused about the conception of base change. It seems that it is a general conception. Thank you if you can tell me the general definition of the base change of automorphic representation using the representation language.