The core is not designed to have any currents flow through it. It is however a conducting loop that experiences a changing magnetic field, it will therefore have small currents induced in it - these are called 'eddy currents'.

The core is laminated to reduce these to a minimum as they interfere with the efficient transfer of energy from the primary coil to the secondary one.

The eddy currents cause energy to be lost from the transformer as they heat up the core - meaning that electrical energy is being wasted as unwanted heat energy.

Laminated means 'made up of insulated layers of iron 'glued' together' rather than being in a single solid 'lump'. A laminated core has a higher resistance than a non-laminated one with the same number of domains. It therefore does not get such big a currents induced in it

If you look at the photo below of a school demo transformer you can see the laminations quite clearly.