An assistant bishop in the Anglican Communion is a bishop appointed to assist a diocesan bishop.
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Church of England
In the established Church of England, assistant bishops are usually retired (diocesan or suffragan) bishops – in which case they are honorary assistant bishops. Occasionally active bishops are appointed to be assistant bishops – however, unlike a diocesan or suffragan they do not hold a title: they are not the "Bishop of Somewhere". Some honorary assistant bishops (more frequently in the past, when Englishmen were commonly bishops in the colonies) are bishops who have resigned their see and returned to a priestly ministry (vicar, rector, canon, archdeacon, dean etc.) in an English diocese.
The Assistant Bishop of Leicester is an assistant bishop who is active rather than retired in the Diocese of Leicester. In practice, she or he acts almost exactly like a suffragan bishop (that diocese doesn't have one), whereas he or she is actually a stipendiary assistant bishop. In November 2016, the Diocesan Synod agreed to replace the present Assistant Bishop, after his 2017 retirement, with a new suffragan Bishop of Loughborough, thus ending the last remaining stipendiary assistant bishop's post in the church (following the 2016 replacement of the stipendiary Assistant Bishop of Newcastle with a suffragan Bishop of Berwick.)
Anglican Church of Australia
In the Anglican Church of Australia, the appointments of assistant bishops have been made in accordance with the Assistant Bishops' Canon since 1966. In the Australian dioceses, these assistant bishops function similarly to suffragan bishops in England (the Australian church has no suffragans per se). According to the 1966 canon, while the term coadjutor bishop may be used for an assistant bishop, no bishop may have the right or expectation to succeed to a diocesan see.