I just recorded a 2 minute long video clip with my Sony camera. The output is an .MTS file, which is ~450 MB. What is the reason for that? Could you please recommend a (preferably free) app that I could use to convert it to another file format resulting a much more reasonable file size?
HD video is very, very large at high quality. 450MB for two minutes isn't actually that bad. To put it in perspective, assuming you were shooting 1080P and 24fps, if there was no compression applied, that same 2 minutes of video would be 6 gigabytes of information.
The reason that videos you download or watch on bluray disks are so much smaller is that they are not source video, but rather highly compressed final output video. When you compress video, a lot of quality is lost. It isn't quality that the human eye can easily distinguish, but it is quality that impacts the quality of future encodings and the quality of edited results.
For best quality, you want to take those high quality, large files you captured, edit them to whatever the final output should be and then do a one time compression down to a final output format. That final output won't be suitable for editing, but it will be perfectly suitable for viewing at a much smaller size.
If you have no desire to edit it and simply want the basic video to be smaller, using a free tool like Handbrake or FFMPEG will easily allow you to transcode to h.264 and a much, much smaller file size. I recommend using two-pass VBR to maximize the quality you get for the size.
It is desirable to record and master in the highest quality possible, and only convert to lower bitrates for delivery (if necessary) at the final stage.
450MB for two minutes is 30mbps. That's not particularly high for a capture bitrate; it's a typical capture bitrate for low-cost consumer gear.
It's a lower bitrate, even, than you may find on a movie available on blu-ray.
You don't specify your target format or platform. Do you simply want to share this with friends? If so, uploading to YouTube will take care of all the conversions for you and save you from worrying about additional bandwidth of sharing it with others, as long as you can stand the upload bandwidth. Putting on DVD? I assume not as you would have said so, but the authoring software would be able to do this for you. Converting to an MP4 or MKV for sharing with friends and playing back on the PC or on a mobile device? Then you could use something like Handbrake. However, doing video transcoding yourself when you don't know what you're doing can result in unwanted results - most transcoding tools, unless they're specifically designed for a particular target format or device, will require quite a lot of technical knowledge.