Some authors reserve the term "term" for just variables and abstracts. We'll probably just say "term" and "expression" indiscriminately for expressions of any of these three forms.
Examples of expressions:
x
(y x)
(x x)
(\x y)
(\x x)
(\x (\y x))
(x (\x x))
((\x (x x)) (\x (x x)))
The lambda calculus has an associated proof theory. For now, we can regard the
proof theory as having just one rule, called the rule of **beta-reduction** or
"beta-contraction". Suppose you have some expression of the form: