Ephraim refers to:
the second son of Joseph
the tribe of his descendants
the whole northern kingdom (given that the tribe of Ephraim was preeminent).
Ephraim was the second son of Joseph, born to his wife, Asenath, in Egypt. His older brother was Manasseh.
Manasseh and Ephraim were adopted by Joseph's father, Jacob (Genesis 48:5). They thus shared Jacob's inheritance along with his other 11 sons. They were blessed by Jacob (Genesis 48; Hebrews 11:21) before any of his other children (Genesis 49).
The tribe of Joseph therefore consisted of the two half-tribes of Manasseh and Ephraim. In some situations they functioned as one tribe.
When Manasseh and Ephraim were brought to him, Jacob crossed his arms so that his right hand, and the greater blessing, was given to Ephraim, the younger of the two (Genesis 48:14). Joseph expressed his displeasure at his father's action (Genesis 48:17-18) but Jacob, fully aware of what he was doing (48:19-20), pressed ahead.
It is noteworthy that the blessing of the younger son had been a pattern in the family for four generations: Isaac instead of Ishmael, Jacob instead of Esau, Joseph before his other brothers (Reuben being the oldest but disinherited, Genesis 49:4; 1 Chronicles 5:1). In fact, notice that Reuben's firstborn rights were transferred to Manasseh and Ephraim (1 Chronicles 5:1). And now Ephraim ahead of Manasseh.
Manasseh and Ephraim became the strongest of the tribes of Israel but Ephraim was greater than Manasseh.
His tribe's preeminent position was apparent even by the time of the wilderness wanderings. In the positions in which the tribes camped, Ephraim headed the three tribes on the west side.
Joshua the son of Nun, who led the Israelites into the Promised Land was an Ephraimite (Joshua 19:50). This led to his tribe receiving one of the largest and best allocations of land.
The land of the Ephraimites included Shiloh where the Tabernacle was erected and Ark of the Covenant rested during Joshua's lifetime.
During the time of the judges, Ephraim provided leadership among the ten northern tribes. The sanctuary or temple, where Eli was the priest, was in Shiloh (1 Samuel 1:3).
Samuel was from the tribe of Ephraim (1 Samuel 1:1).
When Israel split into two kingdoms, an Ephraimite official, Jeroboam, became king of the northern kingdom (1 Kings 12:25). The centre of the political and religious life of the northern kingdom was in Ephraim. The capital city, Samaria, was near the western edge of the territory of Ephraim .
Only in the time of David did God reject the Ephraimite line because of the people's sinfulness, replacing it with a line from the tribe of Judah.
After the exile to Babylon, some from Ephraim resettled in Jerusalem (1 Chronicles 9:3)
British Israelism
There are those who believe that the so-called lost tribes of Israel (the 10 northern tribes) migrated to Britain and the Unites States of America, and specifically that the tribe of Ephraim were the ancestors of the British people. That is a theory based on imagination and devoid of evidence but it is still strongly held in some circles.