Hello there, Sunguk.
The following Knowledge Base article should provide some good information for troubleshooting your issue:
iTunes: May be unable to transfer videos to iPhone, iPad, or iPod
http://support.apple.com/kb/TS1497
Specifically:
Even if you download video podcasts from iTunes, individual video podcast authors usually provide video podcasts, and in some cases, these podcasts may not play on your device. If the podcast is correctly encoded however, it will sync to the device without issue.
If you did not purchase videos from the iTunes Store, they may not be in a format that you can play on your iPhone/iPod. In many cases, you can convert them to the correct format using iTunes or QuickTime.
- Using iTunes: Select a video and choose Advanced > Create iPod or iPhone Version
- Using Mac OS X v10.6: Open the video in QuickTime Player and choose Share > iTunes and then select the iPhone & iPod option.
If you're using a Mac with iLife installed, you can also use iMovie to export a movie in an iPhone/iPod-compatible format. For questions on choosing the correct format, refer to iMovie '11: Choosing the correct export option for your iPhone or iPod touch.
Thanks for reaching out to Apple Support Communities.
Cheers,
Pedro D.