A finite dimensional commutative $k$-algebra is étale if it is isomorphic to a product of
separable field extensions of $k$. For any $n \ge 1$, the conjugacy classes of maximal
$k$-tori in $\operatorname{GL}_n = \operatorname{GL}(V)$ are in 1-1 correspondence with isomorphism classes of étale $k$-algebras $E$ of dimension $n$ over $k$.

Here is how the correspondence goes: given a maximal torus $T$ of $\operatorname{GL}(V)$, the Lie algebra $\operatorname{Lie}(T)$ is an $n$-dimensional etale subalgebra of $\operatorname{End}_k(V)$.

Conversely, given $E$ an étale algebra of dimension $n$ over $k$, view $E$ as a left $E$-module.
The module structure determines a $k$-algebra embedding $E \to \operatorname{End}_k(E)$ and hence an injective homomorphism
of algebraic groups $E^\times \to \operatorname{GL}(E) = \operatorname{GL}_n$,
where $E^\times$ is the "unit group of $E$ viewed as an algebraic group". The image of this homomorphism is the desired maximal torus of $\operatorname{GL}_n$.

It remains to see that étale subalgebras $E$ and $F$ of $\operatorname{End}_k(V)$ are conjugate by an element of $\operatorname{GL}_n(k)$ if and only if they are isomorphic $k$-algebras. This follows from the observation that
if $E$ is an étale subalgebra of $\operatorname{End}_k(V)$ with $\dim_k E = \dim_k V$, then viewed as $E$-module, $V$ is isomorphic to the regular representation of $E$.

From the point of view of Galois cohomology, here is what is going on. Write $G = \operatorname{GL}_n$, let $T_0$ be a split maximal $k$-torus, and let $N = N_G(T_0)$. The $k$-variety $\mathcal{T}$ of all maximal tori of $G$ is $\mathcal{T} = G/N$, and there is an exact sequence of pointed sets
$$1 \to N(k) \to G(k) \to \mathcal{T}(k) \to H^1(k,N) \to 1$$
since $H^1(k,G)$ is trivial (Hilbert 90).

Now, $N$ is the semidirect product of the split torus $T_0$ and the symmetric group $S_n$.
Since $H^1(k,T_0)$ is trivial (Hilbert 90 again), and since the quotient homomorphism $N \to S_n$ has a section, $H^1(k,N)$ identifies with $H^1(k,S_n)$, which in turn identifies with the set $\operatorname{Et}_n(k)$ of iso. classes of étale $k$-algebras of dimension $n$.

Thus the mapping $\mathcal{T}(k) \to H^1(k,N) = \operatorname{Et}_n(k)$ is onto,
and by "twisting" one identifies the fibers of this mapping with the $G(k)$-orbits on $\mathcal{T}(k)$; i.e. with the conjugacy classes of maximal $k$-tori in $\operatorname{GL}_n$.