Many older or cheaper phone cameras use a "fixed focus" lens. ie it is always set to focus a specific distance away from the camera. This is usually set to the "hyperfocal distance", ie everything from half that distance out to infinity is in focus.

This depends on just what is acceptable as 'in focus'. But most photos from these cameras will be sharp enough, they will always have a big depth of field. But they may not be able to focus on things a few centimetres away.

Most newer and better quality phone cameras use a lens with auto-focus. eg for the iPhone, all models since the 3GS have auto-focus (at least for the rear camera). They can focus at a specific distance, which can give much sharper photos. So you can focus on something close to the camera, and have more blur in the background, ie a shallower depth of field.

Also phone cameras have improved in other ways. Specifically, the sensor size. eg the iPhone 6 has a 1/3-inch sensor. This is not that big compared to a DSLR, or some compact cameras, but it is much bigger than many older camera phones. A bigger sensor can allow a shallower depth of field (for an equivalent focal length and aperture).