The meaning of “Subhaan-Allaah”
Shaikh Ibn al-`Uthaymeen رحمه الله:
Those who recite this Du`aa are many, but no one understands its meaning except for a very few.
“Subhaanakallaahumma”, meaning: I Glorify you O Allaah! The Glorification means Tanzeeh: to declare Allaah to be free of all imperfections and everything that is falsely attributed to Him and that does not suit His Majesty (such as attributing to Him a son, or trinity etc.).
There are two things which does not befit Allaah:
1) Equating Allaah with the creation.
2) Denying Allaah’s Attributes.
So when you say “Subhaanakallaahumma”, it is like saying: O Allaah! I declare you free from having any likeness with the creation or having any deficiencies in Your Attributes.