Tayammum

Description about Tayammum

 
Allah does not want to place us in difficulty, This is why He made things easy and lenient for us. He allowed us to use Tayammum when we are ill and when we do not find water, to make things comfortable for us and as mercy for us . Allah made Tayammum
in place of Wudu', and Allah made it the same as ablution with water . Tayammum only involves one strike with the hand on the sand and wiping the face and hands.
Hazrat `A'ishah said, "Upon returning to Al-Madinah
 

Madina city

a necklace of mine was broken and lost in Al-Bayda' area. Hazrat Muhammad (pbuh) stayed there and went to sleep with his head on my lap. Abu Bakr `A'ishah's father came and hit me on my flank with his hand saying, `You have detained the people because of a necklace' So I wished I were dead because I could not move the Messenger was sleeping on my lap and because of the pain Abu Bakr caused me. Allah's Messenger got up when dawn broke and there was no water.

 Then the camel on which I was riding was moved from its place and the necklace was found beneath it.
Allah said in
Al-Nisa : 43

If you are ill, or on a journey, or one of you comes from the Gha'it toilet, or from Lamastum women, but you do not find water, then perform Tayammum with clean earth, rubbing your face and hands. Truly, Allah is Ever Oft-Forgiving.

Any type of illness warrants Tayammum, because of the general indications of the Ayah. As for travelling on a journey.
Hazrat Muhammad (pbuh) saw a person sitting a
way from the people and not praying with them. He asked him, ‘What prevented you from offering the prayer with the people, are not you Muslim' He replied, `Yes, O Allah's Messenger! I am Junub and there is no water.' The Prophet said, `Perform Tayammum with clean earth and that will be sufficient for you
Tayammum indicates that Tayammum is a substitute for normal ablution, not that it involves cleaning the parts that normal ablution does. Therefore, it is sufficient in Tayammum to just wipe the face and hands, as the consensus concurs. The face and hands are wiped with one strike on the sand in this case
Hazrat Muhammad (pbuh )said
I have been given five things which were not given to any Prophet before me: Allah made me victorious with fright that covers a month's distance. The earth has been made for me and for my followers a place for praying and an object to perform purification with. Therefore let my followers pray wherever the time of a prayer is due - and in another narration - he will have his means of purity and his Masjid. The spoils of war have been made lawful for me and it was not made so for anyone else before me. I have been given the right of intercession on the Day of Resurrection. Every Prophet used to be sent to his nation exclusively, but I have been sent to all mankind.
We were preferred with three things over people. Our lines in prayer were arranged in rows to resemble the rows of the angels, all of the earth was made a Masjid for us, and its dust was made clean for us when there is no water. Rubbing your faces and hands. Truly, Allah allows us to use Tayammum and to pray after using it when there is no water, to make things easy for us. 

source  : Tafseer  Qurran  Ibne-Kathir