This clause simply counts up to the specified number using an internal temporary variable. The loops

(loop repeat n do ...)
(loop for temp to n do ...)

are identical except that the second one forces you to choose a name for a variable you aren't actually going to use.

This clause stops the loop when the specified condition (any Lisp expression) becomes nil. For example, the following two loops are equivalent, except for the implicit nil block that surrounds the second one:

(while cond forms...)
(loop while cond do forms...)

This clause stops the loop when the specified condition is true, i.e., non-nil.

This clause stops the loop when the specified condition is nil. Unlike while, it stops the loop using return nil so that the finally clauses are not executed. If all the conditions were non-nil, the loop returns t:

(if (loop for size in size-list always (> size 10))
    (some-big-sizes)
  (no-big-sizes))

This clause is like always, except that the loop returns t if any conditions were false, or nil otherwise.

This clause stops the loop when the specified form is non-nil; in this case, it returns that non-nil value. If all the values were nil, the loop returns nil.