In the communist manifesto what did Marx and Engels mean by "Abolition of property in land and application of all rents of land to public purposes"?
Marx and Engels believed that after a communist revolution, all land would no longer be owned by individual people but would be considered common property.
That would mean that private people who make a living from renting the land they own to others would no longer exist. The government might still charge rent to those people who make over-proportional use of land, which creates another source of income for the government which could then be used for "public purposes", i.e. all the stuff a government needs money for (infrastructure, education, health care, defense etc.).
This comes near the end of chapter 2 of the Communist Manifesto, and it's worth looking at the explanatory text that comes just before it (highlights are mine):
We have seen above, that the first step in the revolution by the working class is to raise the proletariat to the position of ruling class to win the battle of democracy.
The proletariat will use its political supremacy to wrest, by degree, all capital from the bourgeoisie, to centralise all instruments of production in the hands of the State, i.e., of the proletariat organised as the ruling class; and to increase the total productive forces as rapidly as possible.
Of course, in the beginning, this cannot be effected except by means of despotic inroads on the rights of property, and on the conditions of bourgeois production; by means of measures, therefore, which appear economically insufficient and untenable, but which, in the course of the movement, outstrip themselves, necessitate further inroads upon the old social order, and are unavoidable as a means of entirely revolutionising the mode of production.
The line singled out — "Abolition of property in land and application of all rents of land to public purposes" — is the first in the list of these despotic actions that need to be taken in advanced nations, in order to break them of the capitalist habit. Effectively this says that private ownership of bourgeois property would be outlawed, and that all rents of real property would be directed to the state and used for public purposes. The rubric 'bourgeois property' means property that is directly or indirectly involved in production at scale, not private property more generally put: i.e., arable farmland, industrial areas, commercial centers, etc, and probably would be extended to conspicuous consumption, like yachts and mansions, which would be converted to some public purpose.
For example, consider a local shopping mall. The mall itself — meaning the building and the land it sits on — would be taken out of the hands of those private investors who currently own and manage it for their own profit. Instead, it would be owned by the community. The shop owners inside the mall would still pay rent, but rather then paying rents set by self-interested private individuals, their rents would be set by the community and go directly into community coffers. The result (ostensibly) would be that rents for shop owners would decrease — the community is more interested in having a healthy selection of shops and services than in milking renters for mere money — and the local community would have some control over what shops were or were not present in the mall, not forced to cope with whatever private investors decided was most profitable.
Marx is correct that it would take despotic moves to convert an advanced capitalist culture to this economic model. But the model itself has some distinct advantages for the community if it could be achieved. It's worth reflecting on...
The first part of the sentence means that all the land owned by individuals and companies must be stolen by the totalitarian government that these two authors were proposing.
Once the land is stolen by the government, it may still be rented to individuals or groups of individuals for a compensation. The second part of the sentence says that the income that the new owner – government – gets from this renting must be spent non-transparently for the whole "public" that is enslaved by this communist government, not for any well-defined goals of any special group of people that was closer or is closer to the land. In effect, it means that there is no longer any owner who would benefit from the land and who would be motivated to nurture the land and/or try to increase the rent in the future.
Unfortunately, these pathological proposals weren't just a theory. In the 20th century, they have been tested in practice in a big portion of the world, the communist bloc. They unsurprisingly led to a degraded efficiency of agriculture, obfuscation of real prices of crops, meat, and food products, need for huge subsidies, evaporation of the people's emotional relationship to the land and all machines used to manipulate with it and the corresponding disappearance of people's responsibility for the state of the land and the agricultural tools, massive unification of the smaller piece of lands that has led to heavy erosion of soil, and lots of other problems of various kinds.