TPS refers to the number of transactions per second that can be performed on the blockchain. For example, in layman terms, increase in TPS means that the number of payments that can be made using the platform in each second increases as well. There are various tradeoffs involved here.
A higher TPS means that more powerful hardware and higher network bandwidth is required to run the blockchain. This means that fewer people can afford to run nodes that form the blockchain network which in turn means more centralization. Solana is one such example; though Solana supports higher TPS, it has expensive hardware and bandwidth requirements.
On the other hand, a lower TPS means that the hardware and network bandwidth requirements are lower. This means that more people can run nodes that form the blockchain network, leading to better decentralization. Blockchains like Bitcoin, Ethereum fall into this category (excluding the proof-of-work mining hardware requirements). The tradeoff is that transaction fees for such networks are high because there are a limited number of transactions that can be performed on the blockchain.
Sharding is one potential solution to increase the TPS without requiring significantly higher hardware and bandwidth requirements. However sharding might not scale well for span-out transactions, such as smart contracts transactions, in which majority of transactions have to go through multiple shards. Sharding in blockchains is also an area that is actively under research from various entities.
Doge Protocol will take a dynamic inference approach to blockchain scalability, by making various parameters such as block size, block time, finality time votable by the network enablers (such as validators). Once voted, the blockchain will switch to the newer TPS model dynamically after a period of N days. This switchover time is in order of days to give all blockchain nodes enough time to adjust their hardware or network configuration. Under certain circumstances, the blockchain will also perform load shedding. The underlying mechanism will be detailed in a follow-up whitepaper.