gesellig
sociable
Describes a person who likes being with other people often and maintains social contacts.
Mein Bruder ist sehr gesellig und kennt in der ganzen Stadt Leute.
My brother is very sociable and knows people all over town.

sociable
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sociable
Describes a person who likes being with other people often and maintains social contacts.
Mein Bruder ist sehr gesellig und kennt in der ganzen Stadt Leute.
My brother is very sociable and knows people all over town.

The adjective 'gesellig' (sociable) is related to the noun 'der Geselle', which used to mean 'companion' or 'comrade'. So the root of the word lies in the idea of community and being together.
Er ist ein geselliger Typ und immer für einen Spaß zu haben.
He is a sociable guy and always up for some fun.
You can recognize the meaning from the context: if 'gesellig' (sociable) refers to a person, it describes their character. If it refers to a situation such as an evening or a group, it describes the atmosphere.
Anna ist eine sehr gesellige Person.
Anna is a very sociable person.
When 'gesellig' (sociable) describes a person, it is often used with 'sein' (to be) or as an adjective before a noun. Typical formulations are 'ein geselliger Mensch sein' (to be a sociable person) or 'von Natur aus gesellig sein' (to be sociable by nature).
Sie ist von Natur aus gesellig und liebt große Partys.
She is sociable by nature and loves big parties.
To describe a pleasant social atmosphere, 'gesellig' (convivial) is often combined with nouns such as 'Abend' (evening), 'Runde' (group/gathering), or 'Beisammensein' (get-together). A fixed expression is 'in geselliger Runde' (in a convivial group).
Lasst uns den Abend in geselliger Runde ausklingen.
Let's wind down the evening in good company.
social
'sozial' and 'gesellig' can both describe a person who enjoys being with other people. In this meaning, they are similar. 'gesellig' sounds especially natural when talking about gatherings, parties, or having a pleasant time with others. 'sozial' is broader and can also mean helpfulness or topics related to society. If you simply want to say that someone likes social contact and does not like being alone, 'gesellig' often fits very well. 'sozial' can also be correct, however, when sociability is meant.

Nach dem Training sitzen wir noch zusammen, weil die Gruppe sehr gesellig ist.
After training, we sit together for a while because the group is very sociable.
Mein Bruder ist sehr sozial und findet in jeder neuen Gruppe schnell Anschluss.
My brother is very sociable and quickly finds his place in any new group.