Welcome to Android Central! I'll add here what you tried to add in a separate Ask a Question post--that you have Samsung Galaxy S2. Please consider registering on this forum so that you can more easily respond to the threads you create!

I deleted that other post, since I'm adding that information here.
There is a very small file size limit (about 1 MB) when sending videos via messaging (MMS), so most videos you try to send will be too large. They usually have to be compressed a lot (thus making it very low-res) or cut off. If you want to send a video, your best bet is to upload it to somewhere like YouTube or your Google+ Photos or Google Drive, then share the link privately with the recipient. You can also send it via Hangouts (which acts the same way--the video is uploaded to your Google+ Photos, then shared privately with the recipient).