Abstraction of the labor contained in commodities is the basis for determining the proportions at which commodities exchange. It is a necessary component of exchange, but not identical with the act of exchange itself.

An exchange is always an exchange of use-values, for as a prerequisite, there must be inequality of use-value. A commodity is only exchanged for a different commodity, never for the same one.

The fact that abstraction is necessary to resolve the proportion at which these different use-values exchange does not eliminate the presence of use-value in the scenario. If I measure the length of the Grand Canyon in American football fields, the football field "figures" as the pure embodiment of the property length, giving expression to the length of the Grand Canyon. The Grand Canyon "figures" as itself. If length is expressed in meters, it is always a relative expression of length in reference to a meterstick, a physical object that we have set apart as embodying a standard length, never an absolute measurement.

It seems like in addition to identifying value with abstract labor, both value and abstract labor are being connected to something very different, concrete human practice.

The starting point of the analysis was concrete human practice. The real act of exchange is a form of appearance of an underlying content, which Marx identified as value. This value is deduced by the logical necessity of qualitative equivalence to resolve the quantitative proportions at which different use-values really exchange in practice.

Let's take a step back and consider what Marx was really getting at with this statement.

The opposition or contrast existing internally in each commodity between use value and value, is, therefore, made evident externally by two commodities being placed in such relation to each other, that the commodity whose value it is sought to express, figures directly as a mere use value, while the commodity in which that value is to be expressed, figures directly as mere exchange value.

We know that commodities are two things, use-value and exchange-value. Wheat is produced for two reasons, firstly for its use as food, secondly for its exchangeability. We know these both to be true because we observe individual acts of consumption (use-value) or exchange (exchange-value). But the unity of these two aspects is not usually apparent in the same moment.

This "internal" opposition is "made evident externally" in the same moment in the value relation. The use-value of one commodity is held up and the question posed, What is the value of this bushel of wheat? This question is answered in the act of exchange, in which another commodity "figures" (is considered exclusively) as exchange value, and gives expression to the value of the bushel of wheat.

When I buy a television for gold, I am interested in the use-value of the television, but only interested in the exchange-value of the gold.

This interpretation is reinforced in Chap.2 with "His commodity possesses for himself no immediate use-value. Otherwise, he would not bring it to the market. It has use-value for others; but for himself its only direct use-value is that of being a depository of exchange-value, and, consequently, a means of exchange. Therefore, he makes up his mind to part with it for commodities whose value in use is of service to him. All commodities are non-use-values for their owners, and use-values for their non-owners.

So when will one of the commodities "figure as mere use value", while the other still "figures as mere exchange value"

When you are using one as a measuring-stick, it "figures as mere exchange value" and it is in the "relative form"