If you've created a video file which will play on your PC then it should play on the recipient's PC. That, of course, assumes that you're watching it with 'bog standard' software, such as Windows Media Player, and that the recipient has the same software on his PC.
So there's no definitee need to change the format of the video file. However, if you've made the recording using the AVI format, the file will be uncompressed and therefore very large. Many mail systems won't permit you to send attachments greater than a certain size, so that could be where your problem lies.
There are two possible solutions that come to mind
Firstly, you could leave the file in its existing format and use a free file transfer service, such as SendSpace:
http://www.sendspace.com/
(The file goes to the SendSpace server and you send a link to the file to the recipient, so that he can download it from there)
Alternatively, you could convert the file to a compressed format (such as MPEG), which you should be able to email conventionally. This might do the job:
http://www.tucows.com/preview/518513
but you should check that the quality of the converted file is acceptable before emailing it.
Chris