gefällig
pleasing
Visually appealing or pleasant; nice to look at.
Das ist ein sehr gefälliges Design für ein Auto.
That is a very pleasing design for a car.

pleasing / obliging
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pleasing
Visually appealing or pleasant; nice to look at.
Das ist ein sehr gefälliges Design für ein Auto.
That is a very pleasing design for a car.

'Gefällig' (pleasing/obliging) is closely related to the verb 'gefallen' (to please) and the noun 'der Gefallen' (a favor). This connection helps you understand the meanings 'appealing' and 'helpful'.
Könntest du mir einen Gefallen tun und mir helfen?
Could you do me a favor and help me?
The form 'gefälligst' is not a polite request, but an impatient or strict command. It is used as an adverb and expresses anger or authority.
Sei jetzt gefälligst still, ich muss mich konzentrieren!
Be quiet now, I need to concentrate!
When 'gefällig' (pleasing/obliging) describes a thing, such as a design or a shape, it means 'appealing'. When it describes a person's behavior, it means 'helpful'.
Die Architektin ist bekannt für ihre gefälligen Gebäude.
The architect is known for her pleasing buildings.
Using 'gefällig' as a question particle, similar to 'bitte' (please), is very formal and often sounds old-fashioned or ironic today. It is hardly used this way in everyday speech anymore.
Schließen Sie gefällig die Tür, wenn Sie gehen?
Would you please close the door when you leave?
please
'bitte' and 'gefällig' can both occur in requests or when offering something. 'bitte' is the normal, neutral, and very common word for polite requests, instructions, and offers. 'gefällig' in this sense is much more limited and often sounds a bit old-fashioned or like a fixed phrase, for example when offering something: 'Noch Kaffee gefällig?' (More coffee?). The form 'gefälligst' is also important: it does not sound polite, but rather strict or impatient. Learners may confuse the words because both have to do with requests. In everyday language, 'bitte' is almost always the safe choice.

Nach dem Essen fragt die Kellnerin: „Noch ein Kaffee gefällig?“
After the meal, the waitress asks, "Would you like another coffee?"
Der Mitarbeiter sagt: „Unterschreiben Sie bitte hier.“
The employee says, "Please sign here."