A statement is a simple sentence which tells us some information (as oppose to asking a question, for example). It is a record of a situation or state, in other words.
The most basic statement is made up of a subject (what the sentence is about) and a predicate (what the subject does or is). This predicate can be as simple as a verb:
{subject} + {predicate}
{subject} + {verb}
Paint + dries.
Queen Victoria + was sleeping.
The man in the large hat + had been dancing.
Of course the predicate can be much larger and include objects and clauses and so on. But these are still, nonetheless, statements.
{subject} + {predicate}
I + painted the wall.
Queen Victoria + told a joke.
The man in the large hat + clapped his hands.
I + feel ill.
Victoria + was Queen of England.
The man in the large hat + became a professional dancer.
The answer + is blowing in the wind.
The man in the large hat + danced on a stage to a huge audience of cheering men and women who threw their hats in the air and whooped with delight each time he pirouetted!
Useful Links
Subjects in English Grammar – a look at what makes a subject in an English sentence.
Predicates in English Grammar – explanations and examples.