You can use \substack
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ A_k = \bigcup_{\substack{I \subset \{ 1,\dots,k \}\\ \text{card} J = K}} B_j\]
\end{document}

If you feel that there is lot of empty space, here is how to get it out. This one uses \mathclap from mathtools.
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[ A_k = \bigcup_{\mathclap{\substack{I \subset \{ 1,\dots,k \}\\ \text{card} J = K}}} B_j\]
\end{document}

Response to comment
It works inside align*:
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align*}
A_k &= \bigcup_{\mathclap{\substack{I \subset \{ 1,\dots,k \}\\ \text{card} J = K}}} B_j\\
A_k &= \bigcup_{\mathclap{\substack{I \subset \{ 1,\dots,k \}\\ \text{card} J = K}}} B_j
\end{align*}
\end{document}
