Transactions Per Second or TPS refers to the amount of transactions a certain blockchain can process. When the various alt-chain originators talk about scalability they refer to how they can scale up the number of transactions they can process in their blockchain.
The lower the TPS the longer it will take for a transaction to settle and vice versa. At the lower end of the spectrum you find Bitcoin which can process up to 7 TPS. At the higher end you find Ripple that can process 1500 TPS, and supposedly scale up to 50.000 TPS, according to Ripple.
Image courtesy Ripple
Note there can be a variety of reasons for why a blockchain does not process a higher TPS then it does, but that does not necessarily mean that it cannot be configured to run at a higher TPS.