Pilgrimage (Hajj) is a once in a life time journey for those who can afford to make it. The destination of the pilgrim is Mecca, Saudi Arabia. It is an annual event which has taken place since the time of Abraham. The following verses are what the Quran says about pilgrimage.
Chapter 2, verse 196
You shall observe the complete rites of Hajj and `Umrah for God. If you are prevented, you shall send an offering, and do not resume cutting your hair until your offering has reached its destination. If you are ill or suffering a head injury you shall expiate by fasting or giving to charity or some other form of worship. During the normal Hajj, if you break the state of sanctity between `Umrah and Hajj, you shall expiate by offering an animal sacrifice. If you cannot afford it, you shall fast three days during Hajj and seven when you return home - this completes ten - provided you do not live at the Sacred Masjid. You shall observe God, and know that God is strict in enforcing retribution.
Chapter 2, verse 197
The pilgrimage is performed in the well-known months; so whoever determines the performance of the pilgrimage therein, there shall be no intercourse, nor fornication, nor quarrelling amongst one another; and whatever good you do, God knows it; and make provision, for surely the provision is righteousness, and observe Me, O men of understanding.
Chapter 2, verse 198
It is no sin for you that you seek the bounty of your Lord (by trade) but when you press on in the multitude from 'Arafat, remember God by the sacred monument. Remember Him as He has guided you, although before you were of those astray.
Chapter 2, verse 199
You shall file together, with the rest of the people who file, and ask God for forgiveness. God is Forgiver, Most Merciful.
As you can see verse 197 clearly says that pilgrimage is to be performed during the ‘well-known months’, plural, meaning more than one, so why does the Government of Saudi Arabia force every Muslim in the world to do it during just one month in the year?
I have never been on a pilgrimage to Mecca so I cannot tell you what it is like. It must be quite a spectacle seeing millions of people gathered in one place at the same time and all there for the same reason, to worship God.
On the Five Pillars of Islam subject page I have posted a link to a website that has lots of information on how to perform the rites of pilgrimage.