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 
http://www.mathunion.org/ICM/ICM1950.1/Main/icm1950.1.0182.0192.ocr.pdf
for the full statement.