The best answer I can imagine for a question like this is to quote the man himself: "The second result of Lefschetz tells us that a necessary and sufficient condition that a 2-cycle $\Gamma_2$ in $V_2$ be algebraic... This result has many geometrical applications... It is clearly a matter of great importance to extend Lefschetz's condition for a 2-cycle to be algebraic. The general problem is as follows...."
See page 184 of the Proceedings of the ICM 1950 for the full statement:
Hodge, W. V. D., The topological invariants of algebraic varieties, Proc. Intern. Congr. Math. (Cambridge, Mass., Aug. 30-Sept. 6, 1950) 1, 182-192 (1952). ZBL0048.41701.
