noun | fawr·muhl ver·uh·fuh·key·shn
Formal verification is like when you're writing a math proof and you have to show your work for every step, even the obvious ones - it's a process of using mathematical methods to prove that a piece of code or smart contract does what it's supposed to do, without any bugs or vulnerabilities. It's like having a super strict teacher check your homework, but instead of getting a gold star, you get a bug-free dApp.
Example
"I wrote a smart contract for a new DeFi protocol, but then I realized I needed to formally verify it or else I'd get rekt by some nerd on Twitter who found a bug in my code. Spent the next three months in a rabbit hole of theorem provers and SMT solvers, but at least now I know my code is bulletproof (I think)."
"Formal verification is like the condom of smart contract development - it's not foolproof, but it's better than raw dogging it and hoping for the best. Plus, it makes you sound like a bigbrain gigachad when you drop it in conversation at blockchain meetups."