Properties of an Ideal Transformer and the reasons behind them
Suppose you have connected a transformer primary to an AC voltage source. There is no load connected in secondary.

In this scenario, you would ideally want no power to be consumed from the source. However, with a finite magnetising inductance this is not the case. According to faradays law, when a voltage is applied across a coil, a finite flux is established in the core. The establishment of flux requires energy in a non ideal material and that is manifested in the form of a current flowing from the source. 

In short, in the non ideal world, the current flowing from the source has two components, one flowing to the load and the other flowing to establish flux in the core. The former component is captured in the circuit model of transformer as a magnetising inductance, although it is a non linear inductance which depends on the material properties.