To add to the excellent explanation by FractionalRadix, it's worth mentioning that sometimes the line between expressions and statements can seem a little blurry (at least to the observer — the language specification will almost certainly define the boundaries clearly and precisely).

For example, in C we have the expression ++i, which means "add one to the value of i and return the new value". This is an expression because it yields a value, but it also makes a change to the program state. Therefore you can use it as a "pure" expression and assign it to something else:

int iNew = ++i; // increment i, put incremented value into iNew

or you can use it as a statement in its own right:

++i; // increment i and do nothing else

Also in C, a simple assignment can be an expression as well as a statement, e.g.

int x = 2; // statement
int y = (x = 3); // y and x are now both equal to 3

Informally, you can think of an expression as something you can (but don't necessarily have to) put on the right-hand side of an assignment operation.

Languages may also differ in which constructs they treat as statements or expressions. In Rust, an if construct is actually an expression, not a statement, and can be assigned as a value:

let x = if (y == 2) { 5 } else { 10 };

If you try this in C you'll get a compilation error because if is a statement and does not evaluate to a value:

int x = if (y == 2) { 5; } else { 10; } // INVALID; won't compile

But in Python, you can't treat an assignment as an expression like you can in C, unless you use a special recently-introduced syntax:

x = 2
y = (x = 3)
     ^
SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='?

y = (x := 3) # x and y are now both 3