The linked article has a simple explanation on it:

What is Taproot?

Proposed in Bitcoin Improvement Proposal (BIP) 341, Taproot is a cutting-edge upgrade to the Bitcoin protocol, driven by three primary motivations:

* Improved Privacy: Taproot ensures that on-chain, every transaction—whether a simple transfer or a multifaceted smart contract—appears identical. This uniformity masks transaction types, thus bolstering user privacy.
* Enhanced Scalability and Efficiency: By optimizing how transaction data is stored and retrieved, Taproot renders transactions faster and more cost-effective.
* Increased Flexibility: Incorporating the Schnorr signature scheme (via BIP 340), Taproot allows for intricate smart contracts on Bitcoin without disclosing unnecessary details.

The rest of the article explains how it affects LN.