Luci, holds can be done on either debit or credit cards. Neither credit nor debit transactions are immediate, since they must first be initiated by the business, then authorized by you, then actually posted to your account (by the bank, I think). That process is normally completed within a couple of business days, but I've never known debit or credit charges to show up on my account immediately. My understanding is that holds on your credit card would happen while that process is incomplete. The hold is money that is earmarked as unavailable, even though it hasn't officially been spent yet. It's similar to a person writing a check and noting that the amount is no longer available to them, even though it takes several days for the money to actually be removed from their account. The difference is that rather than me mentally earmarking $30 for dinner as unavailable, it's the merchant or my bank physically earmarking that $30 as unavailable while the actual charge is pending.
In general, people are unlikely to notice such holds unless they are large (particularly in comparison to the balance available) or they don't get resolved within a few days. I personally only use about a tenth of my available credit at any given time, and only check my account about once a week, so I rarely notice holds. They generally don't affect my ability to use the card, and they usually disappear before I check my recent transactions.
I did have a very frustrating experience with a hold once, though. It was when I'd only had my credit card for a very short time, and so still had something like a $500 limit on it. I had to buy a new battery for my laptop, but the company I bought it from charged me for the battery and then also put a hold for the battery that lasted for several weeks. So for several weeks, I was missing about a third of the credit that should have been available to me. It wasn't the end of the world, since I mostly had the credit card to build up my credit history (rather than because I really needed it), but it was very frustrating and made me very wary about buying things from that company in the future.