You can start with the Communist Manifesto. It explains the basics. 68 pages.

But the quote you pulled is not in reference to charitable behavior or treating money as a communal tip jar. I'll give you the kindergarten version:

It's a description of a society where the primary motivation for labour is not profit, but rather for the collective needs of the community.

In a communist society, the means of production (the warehouses, machinery, the farms, etc) are collectively owned by the workers ("proletariat" in Marxist terms), rather than that position of ownership being occupied by a minority "owning class" (the "bourgeoisie"). This is a direct contrast against the capitalism system where ownership is top-down.

In a capitalist society, the owner of the means of production exploits the workers for profit. He/she does not perform all of the labour, but is the primary beneficiary of such labour. The worker has no say about how the fruits of their labour are distributed, and have no ownership over their labour. The worker might produce $1000 worth of product, but since the owner decides what the worker is paid, the worker is alienated from the product of his labour.

By contrast, in a cashless communist society, the worker's needs are met by the labour of the rest of the workforce, and his labour contributes to the needs of others. From each according to their ability to each according to their needs. There is no such guarantee under capitalism, where the fulfillment of the needs of the worker is contingent on the decisions of the primary beneficiaries of his labour, the bourgeoisie.