Butterfly
The butterfly formation results from making not one, but two large knight's move enclosures from the corner starpoint. It is generally considered to be inefficient, since as it stands the 3-3 point invasion succeeds, while its two wings don't radiate as much power as wider enclosures would.
This shape is referred to as Kannon-biraki in Japanese. Kannon is the Buddhist goddess of mercy (Skt. Avalokitesvara). In everyday speech, Kannon-biraki refers to a type of double (or "French") door, originally used in cabinets containing images of the goddess.
A duller name would be 374473 enclosure. This is one of a number of unusual three-stone enclosures that are being seen more frequently in pro games.
3-3 point invasion
This sequence occurred in a game of Dosaku (in 1678) and also in a game Yu Bin-Seo Pong-su in 2000. White 11 at a, Black at b, White at c sets up a ko; if White wins the ko the damage to Black's position will be serious, so this may almost be a picnic ko from White's point of view.
Switching orientation, if White really wants to avoid ko, she could play 5 here instead for unconditional life. Wait though...what if Black plays at 7?
is the answer.
is forced, whereupon
threatens bent three life, requiring
. Now White unleashes
, forcing
. After the cut of
, Black is in pieces.
Other invasions
In practice, Black probably played at least one of the marked stones as a checking extension against a corresponding white stone. That makes the marked points interesting as possible invasions for White: if they connect out, a weak white group will gain in strength.
Alternatives
Black 1 here is the normal idea. The invasion point at a is then just some bad aji, not something White can use successfully at once.