Video files are relatively complex beasts that have multiple factors contributing to how well they play.
First, a video file has a container format, this is generally indicated based on the extension the file has and simply defines how the file is physically organized. A MOV file is an Apple Quicktime file, an AVI is a windows audio/video file. Other formats also exist such as MP4, M4V, MPEG, etc. You can't simply change the extension in most cases because the files are organized differently and the extension tells the computer which format the file is stored in. Some players are smart enough to figure out what the file actually is by looking at it though, so you won't always have problems when you change the extension.
Next, a video file has what is known as a codec (short for encoder/decoder), the codec is responsible for actually taking the raw video information (which is really simply just a sequence of photos and some audio) and convert it in to easier to store format. Many, many different codecs exist, but the most standard one for HD video is h.264. h.264 defines how the pictures are broken up and stored so that we don't have to store the video uncompressed (which would be VERY large, like 149 megabytes a second large).
Finally, we have a level of compression within that codec. The amount of compression that each codec can apply is often variable (though it varies based on the codec being used). The level of compression balances the overall quality of the video, the amount of disk space required to store the video and the amount of processing power that is needed to decode the video for playback.
For relatively low levels of compression, it is a fairly light processing load, however since much more data is used, you need fast access to the file in order to be able to read it quickly enough for live playback.
For relatively high levels of compression, either the quality of the video must be decreased or the complexity of the compression must be increased. The smaller file size means that less data has to be loaded from disk per second to support live playback, however more processing has to be done to read the more complexly compressed data and get it back to the color of the pixels that should be displayed.
This all brings us back to your original question. Since the video plays back ok on the camera, but you have issues on your computer, it means that you probably have a bottle neck on your computer preventing it from playing back in real time. This could be any of several things. It may be that the video is not compressed enough and your hard drive or system memory is unable to move the data around fast enough for smooth playback, it may be that the video is too compressed and your processor is not fast enough to decode the video on the fly. It also could be that you have a version of the codec that doesn't perform very well and thus results in being overly taxing on the system.
You can make some guesses based on file size or you can look at memory and CPU utilization in task manager to see if there are any obvious bottle necks. You also have a few options for fixing it once you have the source of the problem determined. You may be able to alter the encoding options on the camera to have it use a different level of compression (though this will likely impact video quality as well). You may be able to add either more or faster memory to your computer or use a solid state drive to supply the data faster. If you are processor limited, it's also reasonably low quality loss to transcode a high compression video to a larger, lower compression video. There is still some quality loss, but less so than increasing the level of compression. (Alternately, you can also increase the compression if you are disk speed limited, but this will result in much more severe quality loss.)
As far as trans-coding goes, you can do that through most any video editing package or numerous stand alone packages for encoding video. Quicktime Pro supports transcoding through using Save As, ffMPEG is a free option, though it can be somewhat trickier to learn to use. If you have the Adobe software suite, Adobe Media Encoder is also a decent option. You could also just import the file in to your video editor of choice and then export it again without any editing and it should produce a new video based on what ever export settings you want to use.