To give more details than Miha, the two papers are
(CHI) Whitehead, J. H.C., Combinatorial homotopy. I. Bull. Amer. Math. Soc. 55 (1949) 213–245.
(CHII) Combinatorial homotopy. II. Bull. Amer. Math. Soc. 55 (1949) 453–496.
It was the first paper that developed the notion of CW-complex, and proved their most used properties.
However the roots of these papers go back to very original earlier papers of his developing what is now called “Simple homotopy type”, particularly
Whitehead, J. H.C. On incidence matrices, nuclei and homotopy types. Ann. of Math. 2 42 (1941) 1197–1239.
which introduced the notion of a “membrane complex”, which is basically the notion of a space obtained by attaching cells. But the development of the notion of adjunction space needs a separate account! This last paper was rewritten by Whitehead, using (CHI), (CHII), to become
(SHT) Simple homotopy types. Amer. J. Math. 72 (1950) 1–57.
which became a foundation paper for algebraic K-theory.
The key aspect of a CW-complex $X$ is that you can develop properties by induction on the skeleta $X^n$; for example the topology on $X$ is arranged so that a map $f: X \to Y$ is continuous if and only if the restrictions $f|X^n$ are continuous for all $n$.
It should be useful for students to study adjunction spaces and the case of finite cell complexes from the book Topology and Groupoids.
The paper (CHII) is no less original, but has not been so extensively used; it is I believe important for the future. It contains a theorem determining $\pi_2(X \cup _\lambda\{e^2_\lambda\},X,x)$ as a free crossed $\pi_1(X,x)$-module; this theorem is sometimes stated but rarely proved in texts on algebraic topology. Some main ideas of the book Nonabelian Algebraic Topology (EMS,2011) derive from and considerably generalise this result and put many other results of CHII, e.g. on relations with chain complexes with operators, in a wider context.
Later: Relevant to this paper is the following:
Ellis, G.J. "Homotopy classification the J.H.C. Whitehead way". Exposition. Math. 6(2) (1988) 97--110,
which shows how the work of (CHII) includes work published later by P. Olum and others.