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It states that any equation describing a physical situation carries equivalent units on either side of the equals sign.

An example of an equation which falls under this category is Newton's second law: F = ma, where F describes a force in Newtons, m a mass in kilograms and a an acceleration in meters/second^2. By definition (and by application of this law), a Newton is equivalent to a kg*m/s^2.

Another is a quantity of kinetic energy: E = (1/2)mv^2. E is an energy dimension (let's use Joules as our units), mass can be given in kg and velocity in meters/second. The right hand side therefore carries units of kg*m^2/s^2. Regrouping these gives us (kg*m/s^2) * m. You may recognize the bracketed term from the paragraph above: it is equivalent to a dimension of force, the Newton. We can express this as N*m, which, (when they act in parallel, and they do here) is the definition of a Joule, so dimensions on either side are equivalent.

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what is dimension of homogeneity and application

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Q: What is dimensional homogeneity and application?
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