How do Layer 2 solutions (rollups, Lightning Network) improve throughout?

I’ve been reading a lot about Layer 2 scaling across different chains, Ethereum’s rollups, Bitcoin’s Lightning Network, and others, and I understand the basic idea that they take some activity off the main chain. What I’m still unclear on is how this actually translates into higher throughput. How are these systems able to process more transactions than the base layer while still inheriting its security? And do different types of L2s, like optimistic rollups, ZK-rollups, or payment channels, achieve these throughput gains in different ways? I’d appreciate a clear explanation or any insights that break this down in simple terms.