A variable buy/sell tax is a fee written into a token's smart contract that takes a percentage of every buy or sell, where the contract owner can raise or lower the rate after launch. The general mechanism is explained on the Buy/Sell Tax page.
Because the owner can push the sell tax close to 100%, a variable tax is a common red flag: it can turn a token into a honeypot that buyers cannot sell, or support a rug pull. Checking whether the tax can be changed is part of a rug check.