A catheter in any of the large intrathoracic veins is capable of measuring the central venous pressure. What does this pressure tell us? The CVP is basically the pressure that pushes blood into the right atrium, and since the right atrium doesn't add anything to this pressure until it contracts, the CVP is thus an approximate measure of the right atrial pressure. The normal value ranges between 4 and 10 cm H2O.
It can be useful to know the right atrial pressure in certain circumstances. For instance, in hypovolaemia, the CVP will be low, whereas in fluid overload states (e.g. acute renal failure) the CVP will be high. Similarly, in cardiogenic shock, the CVP will be high, as the heart isn't able to pump blood around well enough, and so the 'back pressure' builds up.
The pulmonary capillary wedge pressure is measured by passing a catheter from the central venous circulation via the heart into one of the pulmonary artery's branches. A balloon is then inflated distally, just proximal to the measuring end of the catheter. This blocks off the pressure coming from the right side of the heart, and therefore only measures the pressure in the column of blood between the pulmonary capillaries and the left atrium. Thus, the pulmonary capillary wedge pressure is a rough measure of the left atrial pressure.
Again, it can certainly be worthwhile knowing this pressure, given certain circumstances. For instance, it helps determine the severity of left ventricular failure, and eluciates the cause of pulmonary hypertension.