The following is predominately from Wikipedia.
135 (ISO 1007) is a film format for still photography. Introduced in its modern form in 1934 it quickly grew in popularity, surpassing 120 film by the late 1960s to become the most popular photographic film format. Despite competition from formats such as 110 and APS, it remains so today.
The film itself has the same dimensions (35 mm wide) and perforations (16 per 72 mm) (KS1870) as 35 mm movie print film but is enclosed in a light-tight cassette to allow cameras to be loaded in daylight. The standard image format is 24 W 36 mm.
With the advent of digital photography, CCD and CMOS sensor made the size sensor issue a little more complex. Camera manufacturers weren't forced to a film size standard, the main constraint was cost. Digital sensor sizes vary, and are typically smaller than the film 35mm standard. Note that some manufacturers, such as Canon, do make a "full size" sensor that is the same size as the image area of a 35mm film camera (24mm x 36mm).