A global citizen is a citizen of the world,  with no special passport or official title. It's about the mindset and actual actions that a person takes daily. A global citizen understands how the world works, values differences in people, takes an active role in their community and work with others to make our planet more peaceful, sustainable and fairer.

The concept of global citizenship is embedded in the Sustainable Development Goals though SDG 4: Insuring Inclusive and Quality Education for All and Promote Life Long Learning, which includes global citizenship as one of its targets. By 2030, the international community has agreed to ensure that all learners acquire the knowledge and skills needed to promote sustainable development, including global citizenship. Universities have a responsibility to promote global citizenship by teaching their students that they are members of a large global community and can use their skills and education to contribute to that community.
Source: United Nations - Global citizenship

U.N. Sustainable Deveopment Goal 4: 
Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all. 
Target 4.7: 
By 2030, ensure that all learners acquire the knowledge and skills needed to promote sustainable development, including, among others, through education for sustainable development and sustainable lifestyles, human rights, gender equality, promotion of a culture of peace and non-violence, global citizenship and appreciation of cultural diversity and of culture’s contribution to sustainable development

Overview & Progress of the SDG4 - here

United Nations defines Global citizenship as the umbrella term for social, political, environmental, and economic actions of globally minded individuals and communities on a worldwide scale. The term can refer to the belief that individuals are members of multiple, diverse, local and non-local networks rather than single actors affecting isolated societies.

Global Citizenship is not a as new as it might look, the concept is found in all cultures and civilizations since ancient times: 

African Philosophy
"umuntu ngumuntu ngabantu"(In Zulu Language)
Ubuntu is an ancient African word meaning "humanity towards others" or "I am because of who we all are".

Indian Philosophy
अयं निज: परो वेति गणना लघुचेतसाम् ।
उदारचरितानां तु वसुधैव कुटुम्बकम् ॥
—Hitopadesha: 1.3.71
Translation: "The thought that one person is related to me and another is not is that of the narrow-minded. For the broadminded, however, the whole world is one family"

Chinese Philosophy
仁 (Ren: “two-man-mindedness”)
‍Analects of Confucius
Definition: “Wishing to be established oneself, seeks also to establish others; wishing to be enlarged oneself, seeks also to enlarge others.” Relationship between two humans: humanity, benevolence

South American Philosophy 
sumak kawsay (In Quechua Language)
In Quechua Sumak Kawsay roughly translates into “good living” or the “good life",  a way of living in harmony within communities, ourselves, and most importantly, nature.

Socrates
"I am not an Athenian or a Greek, but a citizen of the world."
‍—Plutarch, Of Banishment