As in any commercial endeavor there are variations in what it means.
The simplest answer is that it will deliver 30V at up to 5A. In other words you can connect any resistor across the output from infinity down to six ohms and the supply will maintain the voltage at 30V and will not overheat or otherwise behave badly.
But it gets more complicated. Variable voltage supplies are often rated in the same manor. You can set the output voltage for anything between 0 and 30 volts, and it will hold that voltages for loads that draw up to 5 Amps.
But there is more. Some variable voltage supplies are power limited. So after setting the voltage, they can deliver any current which does not make the product of current and voltage exceed 150 Watts. Supplies rated this way have another limit, sometimes explicitly stated, sometimes not. If power were the only limit, you could theoretically have a really low voltage (.03 volts for example) and deliver the power through a really high current - 500 Amps for the 0.03 volt example in a 150 W supply. No supply can deliver an arbitrarily high current so the manufacturer should state what the real limit is, as has occurred in this case.
Finally, I have one supply that specifies its capability in two bands, with one current limit when operating in the lower portion of the voltage range, and a significantly lower limit for voltages in the remaining upper part of the range. A power limit with very low resolution.
If you are heavily dependent on some aspect of this rating then you need to contact the manufacturer and discuss with them what the limits on their supply are. This may involve talking with engineers or other informed parties, not just the marketing department. If that is not possible some testing while monitoring stress on key components of the supply may be in order.