Unitary demand curve: p = 1 - q In my text book, many theories are explained using ad unitary demand curve: a consumer can buy 1 quantity of the product, or none.
The example of the demand function is $ p(q) = 1- q $

but that means if I want to sell one quantity the price should be 0?
I did simply p(q=1) = 1- 1 = 0

What does it mean?
This demand function is just normalized to unit. If you are not interested in the concrete quantity of your demand function, but you are interested how the demand of the specific market is distributed between firms, you can use this simple demand function.

For example, you can consider a normalized demand function in a Bertrand's game. Let's assume the firms are symmetric, there's no capacity constraints. The demand ($D(p_i,p_{-i})$) of firm $i$ is the following:

$$ D(p_i,p_{-i}) =
\begin{cases}
    0       &amp; \quad \text{if } p_i &gt; p_{-i} \\
    1/2  &amp; \quad \text{if } p_i = p_{-i} \\
    1  &amp; \quad \text{if } p_i &lt; p_{-i} \\
  \end{cases} $$