Suppose you want to use $a$ in two constraints as you've written. You want to assume that $l(x_1) = a$ and $l(x_2) = a$, where $x_1$ and $x_2$ are the indices of the two constraints. But $l(x)$ is created by the prover, and they could have certainly chosen an $l(x)$ which evaluates to two different values at $x_1$ and $x_2$. Then you basically have two independent variables instead of using $a$ twice. This is visualised at the top of page 36 in the PDF linked.
Up until that point, every constraint is verified independently. By this, I mean that $l(x_i)*r(x_i) - o(x_i) = 0$ at each index $x_i$, which is checked by ensuring $(x-x_i)$ is a root of the polynomial. Now, we need a way to verify equality of variables between two different constraints. In other words, to somehow establish things like $l(x_1) = l(x_2)$ between different indices.
The way this is done is by further limiting the way the prover can construct the polynomials (e.g. $l(x)$), so they can't just interpolate whatever values they like. One way to do this is by giving the prover different polynomials $l_a(x)$ which evaluate to 1 whenever $a$ is used and 0 everywhere else. For example, a polynomial where $l_a(x_1) = l_a(x_2) = 1$, and is zero everywhere else. Then they can simply multiply this by $a$ to set the same value of $a$ in all locations it is used. To force the prover to use this, we again encrypt it and provide the $\alpha$ shifted version:
$$g^{l_a(x)}, g^{\alpha l_a(x)}$$
(as was done many times previously). The prover can then raise each of these to the power of $a$ to set that value in all places.
If we have another such pair for another variable $d$:
$$g^{l_d(x)}, g^{\alpha l_d(x)}$$
Then the prover can set both $a$ and $d$ and then multiply the encrypted polynomials together (which corresponds to adding the polynomials in the exponents together).
The same is done for $R(x)$ and $O(x)$.
There is one more catch, addressed in section 4.9.3, that allows the prover to add extra things to their polynomials by multiplying by another $g^1$ and $g^{\alpha}$. This is fixed by introducing another secret shift by $\gamma$.
