The Mach principle, although considered to be not well defined, is a good starting point for a description of what causes inertia.
Theorists have disagreed on any one interpretation of the principle so I will use it only as a starting point. Mach got closest to describing how it works by suggesting it was a gravitational force relative to the fixed background of the universe. Here are some quotes from the current wiki page on Machs take on inertia...
"Local physical laws are determined by the large scale structure of the universe"
"Mach's principle says that this is not a coincidence—that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. There are a number of rival formulations of the principle. It is often stated in vague ways, like "mass out there influences inertia here".
Essentially what Mach didn't say but suggests is that it is gravitational effects exerted by the rest of the universe that can effect the local motion of any object. He describes it in vague terms as a physical law. For some reason he couldn't make the final conceptual step to realising the "physical law" was gravity itself.
So, If one were to be floating in space then all the universe mass pulls on you with its gravitational force equally from all directions. You are effectively at the centre of the universe. If you wish to move an object in any direction you have to exert energy to move in that direction. To move left you have to counter the pull from the universe from the right hand side.
An analogy would be being held by strings top, bottom, left and right. If you want to move right you have to exert effort to counter the pull from the string pulling you to the left.
That is essentially inertia!
It is gravity from the rest of the universe making sure you don't move without having to exert energy or force in any one direction. In the same way that one needs to exert energy in one direction up, to counter the local pull of earths gravity down.
