eben has multiple meanings. The first one translates to even, plane. A second meaning is just in a temporal sense.
But this is not what we are interested in here: The usage we are dealing with here is a usage where the word does not appear as a standalone adjective, but is used as an attribute to another adjective and hence functions as a qualifier to the whole assertion. For an example, compare
Es ist so. (It is like that.)
with
Es ist eben so. (It is just like that.)
Here, eben is attributed to the whole assertion. With this usage, eben is untranslatable to an English word but corresponds vaguely to just, simply, plainly. But, as far as I know, there is no counterpart of the German construction in English. Your friend is right, that it adds some emphasis, but there is a more fine-grained meaning than just that. The sentence could be used without eben and would have the same logical value (it would express the same facts), but the social implications would differ a lot. So let's have a closer look.
Synonyms
eben is fully synonym to other German words such as nun mal and halt and einfach. So for instance the following sentences are equivalent
Die Welt ist eben schlecht. Was soll man machen?
Die Welt ist nun mal schlecht. Was soll man machen?
Die Welt ist halt schlecht. Was soll man machen?
Die Welt ist einfach schlecht. Was soll man machen?
expressing something like:
The world is just bad. So, what to do about it?
Logic
eben is used in reasoning to mark an assertion the speaker does not want to justify further with premises. By using eben, the speaker signifies that they do not wish this premise to be questioned. Hence this premise is marked by the speaker as what in argumentation theory is called a "self-evident premise", or a "dogma" - an assertion that is considered so simple and true, that it cannot (and need not) be derived from other precepts. (To understand the special meaning the word "dogma" has here, have a look at Münchhausen-Trilemma) I guess, this notion of simplicity is the reason how the word eben (a cognate of english even) "plain", "plane" has come to be used this way.
Social Function
eben transports the idea that the assertion is self-evident, it is obvious and easy to grasp. Hence eben is used for explanations which are based on a reasoning and facts which the addressee did not see, although they are considered self-evident and simple to recognize by the speaker. That's why the use of eben comes with an attribution of responsibility or even guilt to the addressee, having a subtext of "The current situation you are finding yourself in is your own fault. It results from you not seeing the obvious."
That's why I would translate your example sentence
Schöne Ferienhäuser oder Hotels bekommt man eben nur, wenn man sie rechtzeitig bucht.
with the following English construction. It is not a word-by-word translation, but it tries to catch the conceptualization of the situation that eben beares:
Well, you would have gotten a nice apartment or hotel if you had just booked in good time.
So, using the four-sides-model of communication, eben does not change the logical value of the assertion, it does not change anything of the "Nachrichtenebene" (of the message) but it has a strong influence on the "Beziehungsebene" (the relationship).
Style and Tone
Due to the above, using eben is a way of marking dominance over the addressee and has a (slightly) arrogant tone. It could make the speaker be seen as a know-it-all, surfing on a wave of hindsight-bias. This might be subject to subjective interpretation, but in any case the use of eben expresses reluctance of the speaker to argue about the assertion.