Cameras need light to be able to focus, so the darker it is, the harder it is to focus. More specifically, they need contrast to focus. If it's too dark to see any contrast on your subject, then the camera won't be able to focus.
Most camera will have some sort of 'focus assist'. It might be a small light that lights up when in dark situations, or it might pulse the flash etc. These can help, but may not be ideal in all situations. If you have an accessory flash, that sits in the camera's hotshoe, those will often have their own AF assist light.
As mentioned, a 'fast' lens (large maximum aperture) will let in more light, which can make it easier to focus. They can also allow you to use a faster shutter speed, and slow shutter speeds may be the reason for your blurry shots, not just missed focus.
But you still have to consider that it's just too dark to get sharp photos, unless you use the flash. So using flash would probably be a good idea anyway.
To help you focus in these dark situations, you could try using a flashlight, a video light or even a laser pointer. Something that will put some light onto your subject, which will give the camera something to see & focus on.