According to one view, because it testifies that the people were forgiven for the golden calf. According to another opinion, because it is the repository of the tablets of the testimony.
Despite their apparent divergence, the two explanations in fact tally. The tablets of the Decalogue are “tablets of testimony” because after the first tablets were smashed in Moses’ indignation at the golden calf, new tablets were given as a sign of God’s forgiveness. When was the forgiveness complete? When the people exerted themselves for God and built the Tabernacle and God signified His approval.
What do we learn? That though the synagogue, like its ancient forebear, houses the Ten Commandments, it needs something more. It needs God’s approval. Approval of the architecture? Partly. The siddur, the services, the ceremonies, the songs? To some extent. But the real question is the people and what they are prepared to do for Judaism and for God.
Do they yearn to feel they are in the Divine Presence? Are they suffused with joy at being able to sing to the Almighty? Are they ashamed of the things that ought to make them ashamed, and confident that with God’s forgiveness they will be able to elevate themselves spiritually, morally and ethically?
If this is the sort of people they are, their synagogue is testimony to their devotion and evidence of Heavenly approval.