Consider the torus $T=\mathbb C^n/\Lambda$ for some lattice $\Lambda$.
Say that two divisors $A,B$ on $T$ are linearly equivalent if their difference is the divisor of a meromorphic function on $T$. Given $D$ a divisor on $T$ define $L(D)$ to be the $\mathbb C$-vector space of those meromorphic functions $f$ such that $(f)+D\ge 0$ together with the zero function.
It is known that if $f_1,...,f_m$ is a basis for $L(D)$ where D is positive and non-degenerate we have a projective embedding of $T$ into projective space given by $(f_1(z)\theta^3(z),...,f_m(z)\theta^3(z))$ where $\theta$ is the theta-function associated to $D$.
Now I saw on some texts that if we take a positive divisor $D'$ linearly equivalent to $D$ we don't alterate the projective embedding, but I don't understand what it means. Can somebody help me?
P.S : I am not sure what do you mean for "non-degenerate". If $n=1$ and $\text{deg}(D) \geq 3$ then the corresponding map is an embedding, but you can have $D$ strictly positive without having an embedding, for example if $D$ is a point. Also, if you consider a "generic" torus it won't be projective (except if $n=1$). So let me just show that if $D \sim D'$ then the corresponding maps coincide.
$D'$ equivalent to $D$ means that $D = D' + \text{div}(f)$ for some meromorphic function $f : X \to \Bbb P^1$. With this definition is it easy to check that $f L(D) = L(D')$. Indeed if $g \in L(D)$ then $\text{div}(g) + D \geq 0$ by hypothesis and so $\text{div}(g) + \text{div}(f) + D' \geq 0$ i.e $\text{div}(fg) + D' \geq 0$. The other inclusion is similar.
In particular, if $[f_1:\dots:f_m]$ is the map corresponding to $D$ then the map corresponding to $L(D')$ is $[ff_1:ff_2: \dots : f f_m]$ but since we are in projective space the two maps coincide.