The blockchain trilemma refers to the design choices that each blockchain has to make. It's about finding a balance between scalability, security and decentralization. Ideally, a blockchain is super scalable, secure and decentralized. In practice, you can’t have it all.
There is no solution or magic bullet to the blockchain trilemma (a term coined by Ethereum co-founder Vitalik Buterin). Just like with any engineering dilemma, trade-offs are part of the design process. Do you want to make a plane as fast as possible? Then you'll have to limit the amount of cargo and people it can take. Do you want to make a vehicle tackle all terrains with ease? Then it won't beat a Bugatti on a race circuit (if ever a nocoiner mutters: 'Can Bitcoin only handle 7 transactions per second? Visa can do much more!' then these kind analogies might help enlighten him or her: ‘Yes, but Visa is a centralized database with absolute censorship power'.)
At first, it may seem counterintuitive that a great invention in the digital realm (blockchain technology) would have problems scaling. In the normal course of affairs, as a technology becomes more popular, per unit it will become cheaper to mass produce and distribute. This is not the case for transactions on a blockchain. A blockchain that becomes very popular can clog, slow down and become too expensive.