# But she who is a real widow, who is left all alone

"But one who is truly a widow, who has no family"

# has set her hope in God

"confidently expects that God will do what he promised to do" or "fully trusts in God"

# continues in offering earnest appeals and prayers

"continues to make requests and prayers"

# offering earnest appeals and prayers

These two phrases mean basically the same thing. Paul uses them together to emphasize how much these widows pray. 

# night and day

"all the time"