A gyre is another name for a swirling vortex. Ocean gyres are large swirling bodies of water that are often on the scale of a whole ocean basin or 1000 s of kilometers across (hundreds to thousands of miles across).
Lean meats are meats with a relatively low fat content. Skinless chicken and turkey and red meat, such as pork chops, with the fat trimmed off are examples of lean meat.
Lean is an expression given to any noun which is pure, trustworthy and generally not full of shit. Derived from the term to describe a non-fatty piece of steak, lean can be extended to describe a person for example. That guy is lean bro, meaning he is not full of shit and he is a cool guy.