The basic concept of statement (or proposition) used in logic is the following :
A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both.
In the context of natural language, the sentence "It is raining" is a declarative sentence stating a fact that is either true or false .
Regarding "Pegasus exists", Wiki's entry says :
Whether or not the sentence "Pegasus exists." is a statement is a subject of debate among philosophers. Bertrand Russell held that it is a (false) statement. Strawson held it is not a statement at all.
The example is a little bit controversial, because it involves a proper name without reference, and this case is a little bit troublesome for standard logic.
We can consider the original Russell/Strawson example :
"The present King of France is bals [wise]."
According to B.Russell in On Denoting (1905) the sentence is significant and false (there is no King of France today), while for Strawson in On Referring (1950) the sentence "is certainly significant; but this does not mean that any particular use of it is true or false."