I read an article that bitcoin transactions are coming in at an overwhelming amount, causing transactions to be delayed.
This is a complicated question, and I probably won't be able to provide a sufficient or thorough answer here.
There are two possible "delays" that a Bitcoin transaction may deal with:
1) The normal block confirmation delay. This is by design. A Bitcoin transaction isn't considered "confirmed" until it is added to a new block in the blockchain, which happens on average every ten minutes. A transaction may be accepted before this happens, but the receiver is then assuming some degree of risk, so it is a policy of the business. This, for example, enables someone to pay for a coffee with Bitcoin. The payment happens instantly, but the coffee seller doesn't have "confirmation" that it was truly valid until the first block. For some use cases, this risk is manageable.
2) The "congestion" delay caused by too many transactions on the network. This is not by design, but occurs because the Bitcoin network has a maximum transaction capacity. When this occurs, transactions can get delayed for hours or days. Those who know how to use Bitcoin competently can usually get around this by increasing the transaction fee they pay, which will prioritize their transaction - so there is always a way to get a transaction to confirm quickly if one is willing to pay (perhaps $0.40 fee instead of a more normal $0.03, for example). Long term, there are ways to scale Bitcoin to resolve this issue so that more transactions can occur on the network, but they are hotly debated (it's a case of too many good solutions, nobody can agree which one to pursue). This has been a huge challenge for the Bitcoin community for the past year, with no end in sight.
Ultimately, open-source software projects like Bitcoin tend to navigate around problems, but it can take a while. Transaction scalability is one of Bitcoin's most significant growing pains.