The AC unit pulls the air in from the room and cools it internally. Once it is chilled it sends that chilled air back into the room. If that was all the AC needed to do, things would be pretty simple and portability would be absolute. However, there is more to it:
As a by-product of the nice chilled air produced inside an AC unit, there is a roughly equal amount of hot, moist air also produced. That hot moist air is definitely NOT wanted inside the room being cooled, because it would counter the effect and actually cause a net heat increase!
So the hot and moist air must be vented out of the room somehow. That is the job of the flexible exhaust hose, which connects to a window kit or wall vent, depending on what the room has available and the unwanted hot air is pumped outside.
Some portable AC units may have two different hoses that connect to the outside. One hose is used to remove heat from the room. The second hose is used to draw unprocessed air in from outside to aid the cooling process inside the unit.
Units with a single hose use it to exhaust hot air to the outside, while air is drawn into the unit directly from inside the room. This can be less efficient than using outside air, but cuts down on manufacturing costs. Also, while one hose may not look so pretty, it's somewhat prettier than two hoses!
If there is any kind of problem with a vent hose, such as a blockage or cracking, the result could be overheating of the unit or hot air being leaked out into the room.
You may also notice an unusual sound coming from the unit's motor. The first thing to do is to check the hose for any kinking or damage, especially cracks or holes causing air leaks. Also, check to ensure the hose is firmly attached to the rear of the unit and similarly firmly attached to the window fixing kit or vent opening.
If you determine that the hose is damaged in some way, it may need to be replaced. Fortunately, it is relatively easy to order a replacement hose from the dealer or store where you purchased the air conditioning unit from, or direct from the unit's manufacturer if necessary. You can usually install it yourself fairly easily by simply removing the damaged hose and fitting the new hose in its place.
If you run into problems that you are not able to diagnose yourself, it's always a good idea to contact the dealer or the manufacturer's technical help line. There is generally a troubleshooting guide in the handbook or you can ask questions on the manufacturer's website.