Albert Barnes Commentary Jeremiah 13:11

"For as the girdle cleaveth to the loins of a man, so have I caused to cleave unto me the whole house of Israel and the whole house of Judah, saith Jehovah; that they may be unto me for a people, and for a name, and for a praise, and for a glory: but they would not hear." — Jeremiah 13:11 (ASV)

The reason why the girdle was chosen as the symbol. Similarly, Israel was the people chosen and set apart so that in them and by them the Holy Spirit might work for the salvation of mankind.