Negative temperature means that the system loses entropy if you put more energy in. This means that negative temp is hotter than any positive temperature, in the sense that if you put two systems in thermal contact, heat will flow from negative to positive.
In the continuum of temperatures, positive absolute zero is the coldest, going up to positive infinity Kelvins. Then minus infinity Kelvins is just slightly hotter than positive infinity. Then it keeps going up to negative absolute zero, the hottest temperature.
These infinities keep cropping up because the reciprocal of temperature is actually the more fundamental physical quantity.