I think it means something like they were meant to be together and when they had sex the bond created. And when you're bond then it's unbreakable and you and your mate have to be together for the rest of yours lifes. And when you aren't, you will feel like missing half of yourself, you'll be lonely, getting weaker and it can end with a death. Or that's how I understand it. But I can be wrong so sorry if I misunderstood the whole thing about bond. :))
You can read the details here
http://www.mangago.zone/read-manga/abarenbo_honey/nbt/6d5913acc7b0dbb2/ChChapter_1/6/
A bond is created when the alpha bites the neck of the omega, when he does that, the omega can't have sex with anyone else
it's a set soul mate kind of thing. it's unbreakable and unpredictable. I guess you could say it's like a alpha marking his omega, where the omega becomes only his and can't mate with other alphas or betas anymore because he'll get sick. Also when a omega is marked they by force need their alpha when in heat because then it becomes painful. though in this story, both are affected which is why they named it "bond" their bodies are now one and they need each other to live on, neither can sleep with someone else and are forced to stay together.
What's with the "bond" thing? I'm new to this series so I'm kinda confuse