A manger is the name for a piece of 'furniture' in a room designed for feeding animals. It is not the room itself.
Many people connect the word manger with the birth of Jesus. But the word manger does not tell us about the room, or even the nature of the manger. Some mangers of this age were stone troughs, most were wooden racks. Iron was such an expensive material at this time that a manger of iron would have been very uncommon.
So we are left with the idea that it was a simple feeding rack, in which there was straw. Now at this time, straw was a common bedding material for all peasants. They lived in a simple single room and put a blanket over a pile of straw to sleep on, then pushed it all to the side of the room during the day. So you must not get the idea that this was especially humble. It was how most people lived. Even if Mary and Joseph had been in an 'inn' they would most likely have slept on straw on the floor. Beds as we know them were not in general use for another 1500 years (for example see the books on Tudor times when that change began to happen in England).
In the times of Jesus, people were much less worried about how they used their rooms, and belongings in general, than we are. But you can imagine that the laying of Jesus in a manger would suggest that He was one of the peasants (the people) and not one of the nobles, that is He belongs to all of us, not just a few.