The vacuum pump in a diesel engine is used primarily to provide enough suction to provide the power brakes. In some engines it also provides power and suction for the A/C and ventilation systems. The vacuum pump is running all the time the engine is running so they do fail sooner or later and give off some very distinctive signs.
The Brakes Get Harder
A vacuum pump failure will cause the brakes to become much harder to push than usual. The vacuum pump provides the suction needed for the power brake booster to function correctly so if the vacuum pump fails, the power brake booster will stop working as well and the brake boost will be lost. The brakes will still work but they will feel hard. Brakes that are gradually getting harder to push can be a sign of a vacuum pump beginning to fail.
Lack Of Suction
Remove the hose from the vacuum pump while the engine is running and place your finger over the hole you should feel a strong suction. If you feel little or no suction then you may need to replace the pump. If you feel the strong suction at the vacuum pump but still don't have any braking power then check elsewhere in the system for leaks.
Open the bonnet and locate the vacuum pump. Look around it for any oil leaks as they may indicate a problem with the seal. You can also listen for any hisses or whistles that may indicate air coming out although they will be hard to hear with the engine running.