It is customary to say some words of praise and respect whenever we mention the name of God 
or the Prophet Muhammad 
. I have added these as little images inline with the text showing the Arabic script for these words, and this is a brief explanation of what they mean and their significance.
There are several words that can be used to praise God (Allah) . One of the most common is "Subhanahu wa Ta'ala". "Subhanahu" is an Arabic word used only with Allah , and it roughly means to state His grace and glory and His refinement from any impurity. "Wa" means "and", and "Ta'ala" roughly means to state that He rises above all His creatures, and above any imperfection.
This statement "Salla Allahu 'Alayhi wa Sallam", is easily translated to "may God pray upon him and grant him peace". Equivalently we can say "'Alayhi-Salatu wa-Salam", which is "prayer and peace upon him". There is a saying of Prophet Muhammad that he told his companions, "Do you know who is the ungenerous person? He is the one who I am mentioned to and does not pray upon me."
The concept of us or God "praying upon" a human being may seem strange at first, especially for a religion that does not deify the Prophet . But it is easily understood when we examine the difference between "praying upon" and "praying to". We pray "to" nobody else but God , that is we talk to Him and ask for His care and blessings. But we can pray "upon" a deceased person at funeral, our Prophet , or possibly anyone else, that is, we ask God to grant His blessings upon that person. When we talk of God "praying upon" anyone, this means He is just directly granting His blessings to that person. Thus, this statement is just a greeting to Muhammad , and since he is the representative of our Islamic nation, any blessings that God grants to him are reflected upon ourselves.
We also pay the same respect and greetings to all the other prophets (Adam, Jesus, etc.) when they are mentioned by saying "Alayhi-Salam", that is "peace upon him". We don't need to ask for the prayer upon them (but it's acceptable to do so) because we already do that through the representative Muhammad .
and Muhammad 
