In biblical times, Jewish men wore a garment called a talith, talit (Pronounced tah-leet) or prayer shawl all the time – not just at prayer. Talith contains two Hebrew words; tal meaning tent and ith meaning little. Thus, you have “little tent.” Each man had his own little tent.
The apostle Paul was a Pharisee, but also a tentmaker (Acts 18:3). Many believe that he made Prayer Shawls, not tents to live in. Training and intensely specific skills were needed to make an acceptable talit-- and a lengthy article could be written on that topic alone.
Six million Jews could not fit into the tent of meeting that was set up in the Old Testament.
Therefore, what was given to them was their own private sanctuary where they could meet with God. Each man had one. It was his Prayer Shawl or Talit. They would pull it up over their head, forming a tent, where they would begin to chant and sing their Hebrew songs, and call upon Elohim, Yaweh, Adonai.
It was intimate, private, and set apart from anyone else – enabling them to totally focus upon God. This was their prayer closet.
[The jury is still out on this interpretation of "closet/tent," but I think it has some merit because in Biblical times, regular tent making was the work of women. Praying under a talit would have diminished outside distractions and certainly may have helped the one praying to maintain a deeper focus.]