$G$ is a totally ordered abelian group if $G$ is abelian and has a total order $<$ such that $g<h$ implies $g+u<h+u$. I have found the following statement in Marker's book Model Theory An Introduction in page 80.
Every ordered divisible abelian group is elementary equivalent to $(\mathbb{Q},<,+)$.
I'm not an expert in logic, but what does the theorem mean? I understand that some statements about $(\mathbb{Q},<,+)$ are true also in $(G,<,+)$, but what kind of statements? It says that statements that are $\mathcal{L}-$sentences, but I'm confused. How can I distinguish $\mathcal{L}-$sentences from those who are not?
Although a very nice answer is provided in Reveillark's comment, I'm going to develop a bit more the ideas here, specially the background motivation, as it seems to me that the confusion stems from the ideas behind the notions, not the notions themselves; moreover, I will refer to Marker's book when needed.
As you probably know, a language $\mathscr L$ consists of a bunch of function, relation and constant symbols (Definition $1.1.1$) and an $\mathscr L$-structure is just a set together with interpretations for these symbols (Definition $1.1.2$). Now the point of these constructions is that many mathematical structures can be regarded as certain $\mathscr L$-structures over some language $\mathscr L$, and this is why the main goal of model theorists is to study these $\mathscr L$-structures and their properties. To do so, one needs a way to name elements of these $\mathscr L$-structures and also a way to say which (first-order) properties these elements have; the individuals of an $\mathscr L$-structure are given by the interpretation of $\mathscr L$-terms (Definition $1.1.4$), and to express statements about such individuals one uses $\mathscr L$-formulas (Definition $1.1.5$).
Now, as explained after Definition $1.1.5$, $\mathscr L$-formulas can either have free variables or not; in the latter case, we say that an $\mathscr L$-formula is an $\mathscr L$-sentence. What is the point of this distinction? Well, note that since an $\mathscr L$-sentence $\phi$ has no free variables, for any $\mathscr L$-structure $\mathscr M$ we have that either $\mathscr M \models \phi$ or $\mathscr M \not\models \phi$; in other words, an $\mathscr L$-sentence expresses a property of the whole $\mathscr L$-structure!
Therefore, saying that two $\mathscr L$-structures $\mathscr M$ and $\mathscr N$ are elementary equivalent (aka $\mathscr M \equiv \mathscr N$, aka $\mathscr M$ and $\mathscr N$ satisfiy the same $\mathscr L$-sentences) expresses the fact that at the level of $\mathscr L$-structures they satisfy the same (first-order) properties. But beware, this doesn't mean that all their elements satisfy the same properties! This is, $\mathscr M \equiv \mathscr N$ doesn't generally imply that $\mathscr M \cong \mathscr N$, where $\cong$ means isomorphism of $\mathscr L$-strucutures (i.e. that $\mathscr M$ and $\mathscr N$ satisfy the same $\mathscr L$-formulas). The converse however is easily shown to be true; i.e. if all elements of $\mathscr M$ and $\mathscr N$ satisfy the same (first order) properties, then $\mathscr M$ and $\mathscr N$ satisfy the same properties as $\mathscr L$-structures.
In conclusion, one could say that $\mathscr L$-sentences enable us to see which properties does an $\mathscr L$-structure satisfy as a whole, while $\mathscr L$-formulas with free variables enable us to discern an talk about properties of particular elements in an $\mathscr L$-structure.