How exactly do "sync committees" help a light client sync up in Eth 2.0 Altair hard fork?

I've read a few things in github about "sync committees" in Eth 2.0 Altair hard fork. For example:

https://github.com/ethereum/annotated-spec/blob/master/altair/beacon-chain.md#sync-committee

allow light clients to easily sync up with the header chain with very low computational and data cost. The goal is to make a light client easy and efficient enough that it can be run inside any environment (mobile device, embedded hardware, browser extension, and even inside another smart-contract-capable blockchain)

Also saw some code here:

https://github.com/ethereum/consensus-specs/blob/dev/specs/altair/sync-protocol.md

However it is not clear to me what exactly these sync committees do to help a light client sync (for example, do they store checkpoints from block headers and provide signatures to light clients that the proof of stake consensus has evolved correctly?) And also not clear to me how this ensures that a light client cannot be "fooled" by an attacker to accept a fabricated chain.