A bit of a detour first.
What is the meaning of Chaotic and/or Evil alignment?
There are a lot of pre-conceptions and caricatures with alignments in D&D, and part of session 0 should be to agree as a collective how each alignment should work in the campaign.
My personal take on these alignments are that we are talking about either the Lawful-Chaotic axis or the Good-Evil axis.
I see the Lawful-Chaotic axis as a needle on "plays by the rules". At the extreme, a fully Lawful character (think Construct from Mechanus) will always play by the rule, even when rules do not totally make sense, while a fully Chaotic character will completely ignore the rules.
I wish to note that there's a big leap from "ignore the rules" to "kill everyone in sight" or "kill whimsically". And importantly, the absence of rules does not mean an absence of goals: the character will still work towards short-term goals (a warm dinner & bed tonight) and long-term goals (being recognized as the Champion of Flip Flop Juggling).
The presence of goals matters because a Chaotic character can still be level-headed, for example, and a level-headed character will not typically take actions that go against their goals. Of course, a character in thrall of their emotions (temper, temper, ...) may accidentally do so, or a not so smart character may without realizing do so, but those are unintended.
Similarly, I see the Good-Evil axis as a needle on "worries about others". At the extreme, a fully Good character will be extremely selfless, regularly going against their goals/comfort to help others achieve theirs, while a fully Evil character will simply not care and generally treat strangers as tools (emphasis on strangers, Evil can have friends).
Once again, there's a difference between "not caring" and "killing on a whim". A Lawful Evil character could be perceived as a wonderful Duke, even if perhaps a bit tough on crime, if the character had realized that mid-term/long-term wealth was better served by a happy people, and worked to improve the standard of living, encourage artisans and merchants, etc... Their "Evil" alignment only means that they are ready to kill/make suffer if doing so furthers their ambitions; but that's only one tool in the toolbox, it need not be the only one they wield.
And thus, once again, we are back to goals, and the means to achieve them. A level-headed Evil character will not slaughter or enslave everyone within sight if they have determined that doing would undermine their goals. They may accidentally do so (emotions) or may not realize the consequences of particular actions (lack of foresight), but those are once again unintended.
How to add meaning to an Evil campaign?
By adding meaning to each character first, as usual. D&D 5.0 has a framework to assist: the Ideal and Bond of the character backgrounds, and to a degree its Personality and the Reason they picked a certain class, are tools to help shape the goals of a character.
From there on, there is not much difference between an Evil group and a Good group: why does a Good group stick together instead of each going their separate ways?
And the answer is that the players wish to play together and therefore shape their characters to do so: they find common goals, form meaningful relationship (Evil can have friends!), and thus make up reasons to continue working together and solving the challenges thrown at them together.
The fact that they are Evil may alter the relationships between them (utility rather than appreciation) and that's fine, it serves the game just as well.