My question is what does it mean? Does it mean that it is simply an isolation transformer? Or is it in some way used for impedance matching?
It is an isolation transformer. It is for isolating signal lines with a characteristic impedance of 600 Ω. This may include audio and telephony circuits.
simulate this circuit – Schematic created using CircuitLab
Figure 1. Using a 1:1 transformer to "unbalance" a balanced microphone for an unbalanced input while maintaining balanced operation over the length of the cable.
Signal level transformers have many uses such as isolation, ground loop prevention, differential signals, etc. Professional microphone and audio signal applications account are among the common applications where using various schemes are used to reduce any common-mode noise. As can be seen in Figure 1, any common signal on the two mic lines will be rejected by the transformer as it will only pass differential signals.
How can it be used for impedance matching if both the primary and secondary have the same resistance?
The impedance matching is required when both circuits are 600 Ω and isolation is required.
Lets say for example I have constructed an amplifier with output impedance of 600 ohms. The speaker has an impedance of 4 ohms. How can this transformer be used to match the impedance?
It can't. In any case, a 600:600 Ω transformer would be for mW signal levels and not 0.5 to 20 W levels, for example.