The $h$-principle also known as homotopy principle applies to partial differential relations (PDRs) for which any underlying formal/algebraic solution is homotopic to a real one. The $h$-principle allows to boil down a differential topological problem to a topological one.
Let $M$ and $N$ be two manifolds, a partial differential relation $R$ of order $k\geqslant 1$ is a subset of the fiber bundle formed by the $k$-jet extensions of $C^k$-maps between $M$ and $N$, namely $R\subseteq J^k(M,N)$. A solution of $R$ is a $C^k$-map between $M$ and $N$ whose $k$-jet extension belongs to $R$, whereas a formal solution of $R$ is only a section of $J^k(M,N)$ whose image lies in $R$. In that context, one says that $R$ satisfies the $h$-principle if and only if any formal solution of $R$ is homotopic to a solution of $R$ in the set of formal solutions of $R$.
References.
Y. Eliashberg, N. Mishachev, Introduction to the $h$-principle, American Mathematical Society, 2002.
H. Geiges, $h$-principles and Flexibility in Geometry, American Mathematical Society, 2003.
M. Gromov, Partial differential relations, Springer, 1986.