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.).
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.