Leftwards double arrow

B is enough to guarantee A. Read A ⇐ B as “A if B”, “A follows from B” or “A is implied by B”. Example: x > 2 ⇐ x > 5. Any number above 5 is certainly above 2.

It is exactly the same statement as B ⇒ A, just written with the conclusion first. In the language of conditions, B is a sufficient condition for A, and A is a necessary condition for B. It says nothing about the other direction: x > 2 does not make x > 5.

Its most common home is the “if and only if” proof. To show two statements are equivalent (⇔), you prove both directions, and textbooks label the halves (⇒) and (⇐). The (⇐) part starts from the right-hand statement and proves the left one.

Is it ever just an arrow?

Yes: outside math it simply points left. In notes, signs and menus people use ⇐ as a heavier ←, to point back at something or to mean “back”. In that setting it carries no logic at all.

Its logic job is younger than it looks. Arrows for implication appear in formal logic by 1922, and the double-shafted form by 1954; the double shaft keeps “implies” apart from plain single arrows, which mathematicians use for limits and functions.