What are pending Bitcoin transactions?
The Bitcoin electronic (AKA Cryptocurrency) is a distributed form of currency. This means that all transactions must be distributed among the distributed chain. These are mathematically confirmed transactions that take time to produce.
When transactions are not processed at the same rate as transactions are done, then this amounts to delayed Bitcoin transactions. In practice it means that transactions done now will take some time to process. This is severly limited by the rate transactions can be processed by the Network.
In December 2017 the Bitcoin mania is at it's peak and with a lot of sellers and buyers in the market, the number of delayed transactions has passed 200,000 transactions on many days. While the network can process an average of 24 transactions / second, it can be a substancial delay.
Payments will always eventually be processd, but this is one of the underlying issues in the technical design of Bitcoin as a liquid currency. Consider this difference in scale between Visa credit card transactions in the Wikipedia article on the Bitcoin Scalability problem:
Bitcoin blocks carry the transactions on the bitcoin network since the last block has been created. In contrast to Visa's peak of 47,000 transactions per second, the bitcoin network's theoretical maximum capacity sits between 3.3 to 7 transactions per second.
When you are trading Bitcoins in an exchange this delay does not take place as the trades are not done in the public blockchain - rather simply inside that specific Bitcoin exchange. You can track live statistics of pending transactions and transactions fees at blockchain.info/unconfirmed-transactions