Yes, Judaism does have meditation within its culture, but it's not mainstream, and it's certainly not an essential part of our religion. Neither, however, does Judaism reject meditation, except when the meditation theories start talking about divine consciousness, chakras, energy sources, and so on.
Let's just say that I, one of the least spiritual of human beings, have integrated meditation into my life. But there's nothing mystical about it. It's just my way of finding a little peace. If you've ever shut the door and curled up with a good book, or taken a long bubble bath, you've done the same thing. It's that mundane.
Imagine that you just step onto a boat. The constant rocking of the boat is fine to start with, but eventually you become out of balance. Not immediately, but gradually, little by little, your sense of control erodes, until you're nauseous. As long as the boat keeps rocking, you can't find your footing. You need a breather, just a few moments of no rocking to re-find your balance and settle your stomach. Then you can get back onto the boat and start over.
The same goes for juggling. When you start juggling, everything is in control. Little by little, the balls begin to drift out of plane, and then you're reaching to try to keep them going. It's the same juggling, but now all off balance. If you stop juggling for a few moment, calm yourself, and start again, you start off in balance.
That's what meditation does for me.
I admit trying to "meditate" when I first got divorced, wondering if there was anything particularly spiritual about it. To do this, I sat in a dark room with a lit candle. I tried to empty my thoughts. No matter how I tried, I couldn't do it.
It's because I'm a measurer. I kept checking myself: are my thoughts empty yet? And, of course, if you are aware of your thoughts, you can't have emptied them. "Nope, not empty, yet."
So that didn't work.
My solution was to stop worrying about if my thoughts were empty or not.
When I meditate now, I no longer need the candle. I just imagine one in my head. I imagine the dark room and the single light, and I concentrate on the light. That's it. My thoughts never empty, or maybe they do, but I don't care.
I don't have to do much to meditate. Just stand or sit still and close my eyes. I imagine the candle. I breathe deeply once or twice. I imagine myself being calm. I let go of emotions and other hooks into my life; actually, I just put them down for a few moments.
After resting for a few moments, I pick them back up, and go back to what I was doing. That's it.
I've found that it makes me pretty calm, most of the time.
Of course, it's not always that simple.
"Daddy! Daddy! What are you doing! Are you me'tating? Are you Daddy? Are you? Huh? Can I me'tate too? Can I? Can I Daddy? Look Daddy! Look! I'm me'tating! Daddy, he's both'ring me! Go 'way! We're me'tating! Can I help you me'tate Daddy? Can I? I can make the me'tating sound! Listen! Are you lis'ning Daddy? Are you? Lis'en. OMMMMMM! Hear that Daddy? I'm helping you me'tate. Aren't I, Daddy? Aren't I? ..."