Imagine that you have a bucket and that your mission is to fill that bucket full with water from a spigot. The fastest way to do it is to fill it with the tap all the way open. If you open the spigot only half-way, it will now take twice as long to fill the bucket. Proportionally, as long as you account for the degree to which you have the spigot open by allowing the bucket to fill for longer or shorter amounts of time, you still end up with a full bucket. Open the spigot only one quarter? No problem, so long as you realize the bucket will now take four times as long to fill as it did with it open all the way. Relationships such as the one between the degree to which the spigot is open and the time the bucket takes to fill are known as "reciprocal."
In much the same way, the basis of exposure is that if you cut the size of your aperture opening in half (which is the same as decreasing your f/stop by one stop) you have to double your exposure time (that is, you increase it by one stop) to compensate in order to get the same exposure. In other words, the relationship between aperture and exposure time is a reciprocal one in much the same way as the one between the spigot opening and the time it takes to fill a bucket with that opening. Whatever you do to one of them, you must do the opposite to the other, and by the same amount in stops. No matter how you get there, proper exposure is achieved when the "bucket" of your film is full.
But what would happen if your bucket had a small hole in the bottom of it? If you fill the bucket fast enough, the hole will have a negligible effect on how long it takes to fill the bucket. But if you take long enough to fill the bucket, the amount of water that would leak out will indeed make a difference. No longer would the spigot opening and the time it takes to fill the bucket truly be reciprocal. You would need to wait longer than you thought for the bucket to fill to compensate for the water that leaked out while you were filling it.
In much the same way, the reciprocal relationship between aperture and shutter speed holds true only for "normal" ranges of shutter speeds and apertures. At longer and longer exposure times, it becomes necessary to compensate for something known as "reciprocity failure," where the reciprocal relationship between aperture and shutter speed begins to break down, almost as if your camera had a small hole in the bottom of it (but don't worry, it doesn't really).
Modern films tend to handle long exposures better than previous generations, but they are not all created equal. Some films are very forgiving of long exposures (they have good reciprocity characteristics), while others are far less forgiving. For example, Fuji Velvia requires an extra 1/3 stop exposures longer than 4 seconds, and even more compensation as exposure times increase from there, whereas Provia F requires no compensation for exposures up to 4 minutes. Older Kodak slide films tended to require compensation for exposures over 1 second, but the newer E100VS is fine up to 10 seconds with no compensation. Both Fuji and Kodak publish exhaustive details on reciprocity corrections for all their films on their websites.
One further point about reciprocity: Color films contain three light-sensitive emulsion layers, which sometimes have different responses to long exposures such that reciprocity can break down at different rates for each layer. Often not a cause for concern, longer exposures may require the use of color correction filters if you want to keep a neutral response. Consult the data from your film manufacturer for specifics since each film is different.