A real transformer delivers less output power than it receives because some input power is converted into heat and other unwanted forms.

Copper loss

Current flowing through winding resistance produces copper loss:

$$P_{\mathrm{Cu}}=I^2R.$$

This loss therefore grows strongly with load current.

Core loss

Alternating flux in the magnetic core produces hysteresis and eddy-current losses. At a fixed supply voltage and frequency, core loss is often much less dependent on load current than copper loss.

Efficiency

Transformer efficiency is

$$\eta=\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}.$$

Equivalently,

$$P_{\mathrm{in}}=P_{\mathrm{out}}+P_{\mathrm{loss}}.$$

A high efficiency means only a small fraction of the input real power is dissipated inside the transformer.

Voltage regulation is different

A transformer can be efficient while still showing a noticeable change in secondary voltage between no-load and loaded operation. This change is described by voltage regulation and is caused mainly by internal resistance and leakage reactance.

Efficiency measures energy loss; regulation measures how well the output voltage is maintained as load changes.