Consider a simple function f(z)=z (usually z is used when we consider a complex number but x is equally ok in this example).
This function has a zero when z=0. If the initial function is something like f(z)=z-a then the function will have a zero at z=a. This function has no poles.
Consider a rational function f(z)=(z-a)/(z-b); this function has a zero when z=a and also has a pole at z=b. The function becomes infinite at z=b. This is a first order pole.
Consider a similar example f(z)=(z-a)/((z-b)*(z-c)); it has two poles at z=b and z=c (also zero is at z=a). If b=c, we will have a second order pole.
In electrical circuits, z can be represented by current and voltage. In AC circuits, both voltage and current are associated with their respective phases and that makes matters interesting...
Perhaps you can now correlated order of filters with poles ...