Fardh is an Arabic world, which means compulsory or obligatory. The Five daily prayer i.e., Fajr, Dhuhr, 'Asr, Magrhib and 'Isha are obligatory prayers. It is a sin to intentionally skip a Fardh Prayer. If a prayer is missed because of forgetfulness or due to some unavoidable circumstances, then offering the missed Prayer as soon as possible will rectify this mistake.
The Holy Prophet, peace be upon him, offered extra Raka'at of Prayer in addition to those of Fardh Prayers. These are called Sunnah Prayers. It is considered necessary by all jurists to offer these prayers. The willful neglect of Sunnah Prayers is censurable in the sight of Allah.
Wajib prayers are necessary and willful neglect is considered sinful. However, if someone misses any of these due to unavoidable circumstances, Qadha (make-up of missed prayer) is not required.
Nawafil plural form of an Arabic word Nafl which means voluntary or optional prayer. One may offer as many Nawafil Prayers as one wish.
However, Nawafil should not be offered during the forbidden times for Prayers. Nawafil should not be offered between 'Asr and Maghrib Prayer. It is preferable to offer Nawafil Prayers at home rather than in a mosque. However, it is matter of personal choice and there is no compulsion in this matter.
Some virtues stated too..
Ibn Salmaan says that he heard one of the companions of the Prophet Mohammad (Sallallaho Alaihe Wasallam) narrating,
"When we had won the battle of Khaibar, we began to buy and sell among ourselves the booty that had fallen to our lot. One of us went to Prophet Mohammad (Sallallaho Alaihe Wasallam) and said, 'O Apostle of Allah , no one else has earned so much profit as I have obtained in today's trade.' 'How much did you earn ? asked the Prophet Mohammad (Sallallaho Alaihe Wasallam) . He replied, 'I kept on selling and buying till I earned a net profit of three hundred 'Ooqiyyah' of sliver.' The...