If you make a definition such as f[x_]:=value, the Wolfram Language will use the value you give for any f function it encounters. In some cases, however, you may want to define a value that is to be used specifically when you ask for numerical values.
define a numerical value to be used when n‐digit precision and any accuracy is requested
Defining numerical values that depend on numerical precision.
This defines a numerical value for the symbol const, using 4n+5 terms in the product for n‐digit precision.
Here is the value of const, computed to 30‐digit precision using the value you specified.
The Wolfram Language treats numerical values essentially like upvalues. When you define a numerical value for f, the Wolfram Language effectively enters your definition as an upvalue for f with respect to the numerical evaluation operation N.