Why do male lions have manes?

Answer: Showing strength to rivals and attracting mates

Blending into tall grass while stalking prey — A mane does the opposite of camouflage: it makes a male stand out, which is one reason lionesses do most of the stalking. The mane's job is to be seen, by rivals and by females.

Showing strength to rivals and attracting mates ✓ — Correct! Long-term studies of Serengeti lions found that the mane works as a billboard. Females prefer males with longer, darker manes, and dark-maned males have higher testosterone, recover better from injury and hold their prides longer; rivals, shown dummy lions, were more wary of dark manes. The older idea that the mane shields the neck in fights has not held up: maned males are not wounded on the neck any less often than expected. The mane costs its owner heat, so it is an honest signal that only a strong male can afford, and in the hottest regions, such as Tsavo, some males grow almost none.

Storing extra fat to survive lean seasons — A mane is hair, not fat, and it stores nothing; lions carry their reserves as body fat like other mammals. If anything the mane is a cost, trapping heat in the sun, which is why males in the hottest, driest places tend to have the thinnest manes.