The .mts is a container file format for multiplexing audio, video and other streams. It is based on the MPEG transport stream container and is also known as BDAV MPEG-2 transport stream. This format is commonly used for high definition video on Blu-ray Disc and AVCHD and HD Camcorders. It usually contain AVC/H264 or MPEG2 video.
Files in AVCHD format use legacy "8.3" file naming convention, while Blu-ray Discs use long filenames. That's why the filename extension of video files is ".MTS" instead of Blu-ray Disc's ".m2ts". Also other files use different extensions: .CPI - .clpi, .MPL - .mpls, .BDM - .bdmv.
Apple's Final Cut Pro can read .MTS files (as stored in Sony HDR camcorders) by using the AVCHD plugin in the Log and Transfer window. Daminion Media Management Software allows to import and manage .MTS & M2TS files.