Film is not as sensitive to light as a digital sensor is – which you are perhaps more used to. To compensate for being less sensitive, and in order to allow enough light in for the photo, the camera can do one of two things, or indeed both – open the lens aperture wider, and/or leave the lens open for longer (i.e. a long "shutter speed").
This is an indoor photo, and even though you might think it's reasonably bright in there, it really is not. (Human eyes are wonderful at adapting to low light.) Your camera is struggling to let enough light in for the photo. Probably the lens is opening as wide as possible, and the camera is additionally leaving the lens open for longer. Despite your best efforts to hold the camera still, this is really an impossible task.
There are a couple of solutions here – one being to add extra light by using a (better, more powerful) flash – but probably the first thing I'd try is to just use a small table-top tripod. Use your camera's self-timer if possible, so that you are not even touching the camera at the moment the photo is taken. This will reduce camera shake and the consequent blur in your photos.
Outdoors in sunlight, you don't need to bother with the tripod usually. Indoors, it will certainly help.