Photos with "bokeh", or soft background blur can't generally be produced with pocket cameras, one of the few downsides to them still*. The bigger the sensor, the easier you can get nice soft background blur. The new mirrorless cameras, like Micro Four Thirds for example, have smaller sensors than traditional film (half the size of a 35mm film frame ("full frame"), linearly, one quarter area-wise), but with the right lens you can still get this effect.
*Even here, progress is made. The Sony RX100 is pocket-sized but still manages to have a sensor large enough to get some background blur if you want.