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](https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1950.1/ICM1950.1.ocr.pdf)
for the full statement:

<cite authors="Hodge, W. V. D.">_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](https://zbmath.org/?q=an:0048.41701).</cite>