Power series in the Wolfram Language are represented in a special internal form, which keeps track of such attributes as their expansion order.
For some purposes, you may want to convert power series to normal expressions. From a mathematical point of view, this corresponds to truncating the power series, and assuming that all higher‐order terms are zero.
This generates a power series, with four terms.
Squaring the power series gives you another power series, with the appropriate number of terms.
Normal truncates the power series, giving a normal expression.