Expressions are strings of mathematical symbols that describe quantities (link: expressions). Want to know how many apps there are for the iPhone? There's an expression for that.
Expressions consist of mathematical operations ( + , - , ×, ÷), numbers (1, 2, 3, etc.), parentheses (()), and variables (x, y, z, etc.). Many different English phrases translate into each of these mathematical symbols. You will find as we go along that there is a distinct relationship between between math and English. It's like they're married: they have a lot in common and you'll often find them together, but each speaks a totally different language.
English is ambiguous in that one word can have two or more meanings, while mathematics is precise and unambiguous. In other words, if we write ×, we mean ×. If you come across the word "times" in English, it could be talking about the time of day, measuring someone's sprinting speed, or referring to a newspaper. English can sometimes be harder to keep up with than a frazzled 6-year-old. Calm down, Billy. Now tell us, where did Shaggy dig up a human femur again?
We can think of translating English into mathematical symbols as clearing away the ambiguity so we can tell what's going on. Lifting the fog. Rubbing the side of our fist across the shower door.