I am having a hard time to understand the meaning of measurements that involve a product of physical units, like $10\, \rm N\cdot m$ ($10$ Newton-meters), $3.33\, \rm J\cdot s$ ($3.33$ Joules-second), and so on.
When I have a quocient of physical units, everything is simple: $10\, \rm m/s$ (meters per second) means that in every one second, I travel a distance of $10$ meters. $25\, \rm N/m^2$ (Newtons per square meter) means that in every square with side equal to $1\, \rm m$ in a surface, I have a force of $25\, \rm N$.
But what does the product $10\, \rm m\, s$ ($10$ meters-second), $25\, \rm N\, m$ (Newton-meters) mean? I just can't figure out the meaning of this even after many online searches.