The classic everyday example of prestressing is this:
A row of books can be lifted by squeezing the ends together:
The structural explanation is that the row of books has zero tensile capacity.
Therefore the ‘beam' of books cannot even carry its self weight. To overcome this we provide an external initial stress (the prestress) which compresses the books together.
Now they can only separate if the tensile stress induced by the self weight of the books is greater than the compressive prestress introduced.
Concrete
Concrete is very strong in compression but weak in tension. In an ordinary concrete beam the tensile stress at the bottom:
are taken by standard steel reinforcement:
But we still get cracking, which is due to both bending and shear:
In prestressed concrete, because the prestressing keeps the concrete in compression, no cracking occurs. This is often preferable where durability is a concern.