I think it means that he established, through his policies, a constituency of support that he would in future be able to rely upon to provide a national majority.
One way this can be done is by appealing to voters who hitherto have never voted - the poor etc. Another way is to capture the centre ground, so that people who had previously voted for your opponents come across. The quintessential example of this was Tony Blair, who reformed the Labour Party in Britain so that it would no longer appeal just to trade unionists, intellectuals, and the marginalised, but to many who occupied the prosperous centre-ground of British society. The result was that in 1997 he won a stunning victory - with a majority of over 160 seats in the House of Commons. He repeated this in 2001, and to a lesser degree in 2005. Blair created a new national majority.
I am not as familiar with Roosevelt's success in 1932 - but I am supposing that it was achieved by appealing both to previous non-voters, as well as to the centre-ground. But from wherever the majority came it won him 4 presidential elections.