A pressure building coil is a length of tubing that takes liquid from the bottom of the vessel, lets it warm and turn to gas, and returns that gas to the top space. The expanding gas raises the internal pressure, and that pressure is what pushes liquid out of the withdrawal line when you open the valve.
Without it, a pressurised vessel has no way of dispensing. There is no pump involved in these systems. The vessel drives its own delivery by deliberately boiling a small amount of its contents, which is why a pressurised vessel always consumes more nitrogen than a non pressurised dewar of the same size.
The coil is controlled by a pressure building regulator, which opens when the pressure falls below the set point and closes when it is reached. Two symptoms point at that regulator. If the vessel will not build pressure, or builds it far too slowly to dispense, the regulator may be closed or the coil frosted and blocked. If the vessel keeps venting through the relief valve when nobody is using it, the regulator may be passing when it should be shut, which wastes nitrogen continuously.
Non pressurised dewars have no coil and no regulator. Liquid comes out by pouring or by a hand pump, as on the CryoCrest dispensing dewars, which use a manual aluminium foot pump so there is no gas pressure to manage while pouring. That is a genuine difference in daily handling, not just a specification detail.