Question

How did Mendel explain that it is possible that a trait is inherited but not expressed in an organism?

Answer 1

Some traits that are inherited may not express themselves. Such hidden traits are known as recessive traits. Mendel explained this phenomenon with the help of monohybrid cross. In a monohybrid cross performed by Mendel, tall plant was crossed with a dwarf plant which produced all tall plants in $F_1$, progeny.
However, when these $F_1$, tall plants were crossed with each other, both tall and dwarf pea plants were obtained in $F_2$ generation. Reappearance of the dwarf pea plants in $F_2$ generation proves that the dwarf trait was inherited but not expressed in $F_1$, generation.
$\begin{array}{ccc}\text{Parent}& \text{Tall(TT)}\times & \text{Dwarf (tt)}\\ & \downarrow & \\ {\text{F}}_1\text{generation}& \text{Tt}& \text{Tt}\\ & \text{selfing}& \\ {\text{F}}_2\text{generation}& \text{TT}\text{Tt}\text{Tt}& \text{tt}\end{array}$

So, dwarfness traits of plants (pea plant) were not lost but are suppressed in the $F_1$, generation and thus reappeares in $F_2$ generation.