Every generation has it's own slang. Every generation develops its own ways of communicating certain issues within the group. What was "groovy" or "awesome" in previous generations is now OMG! and LOL! and will be something else entirely in coming generations. Whether you cringe or giggle when you hear your kids use these words, it's a part of the passing of the torch, generationally speaking. You have little control over the terminology.
How and when kids use these bits of slang, however, can be influenced by you. You as a parent can help your kids understand the time and place to use the current slang - and when not to. What's okay with friends is not so okay with Granny and with an employer or teacher. You as a parent can help your child understand that.
When kids are with friends, they will use their own language whether we want them to or not. If you have talked with your child about basics of communication that span generations - mutual respect, clarity, and the Golden Rule - you can relax a bit and let this happen. Because it will happen.
If you are curious or concerned about the meaning of some words, ask. You may or may not like what they mean, but remember they are not your words. You can express your concern about the meanings and usage, but you likely will do little to change the actual slang.
When kids are communicating with others, however - parents, grandparents, relatives, community members, teachers, and the like - you absolutely can insist that your kids not use their slang. Using accepted words and methods of communication with those outside their generational social circle is totally reasonable and a way of showing respect for those around the - just the kind of respect your kids hope to receive.
Using examples from your own youth may be particularly helpful here. While your child may guffaw at story and the words you used that made your grandmother look at you funny, the point is the same - how to communicate effectively and appropriately across the generations.
Not for parents
Do you remember the first time you heard one of your parents use a bit of your generation's slang? Did it sound weird? Did you cringe? Guess what? If you try to use your kids' slang, they feel the same way. So don't!
Let your kids' slang be your kids' slang. Show a little respect for the changing generations and let your kids' generation have some terminology to themselves. If you want your child to have some respect for your generation and communicate without slang, let that respect go the other way, too. Maybe, if you really love the word and think it apt, you can use it out of their earshot - but keep it out of their earshot. You don't want to look like you are trying to hard to be cool.
No matter what the words are, no matter what the generation, slang happens. Helping your child understand that there's a time and a place to use generational slang is a part of helping them communicate with the world at large.