This has always been a favorite line of mine. As you may know, the word Ebenezer comes from 1 Samuel 7:12. Israel had just screwed up with the ark (the Philistines had captured it) and gotten it back (only because God has freaked the Philistines out by knocking their precious Dagon over), and Samuel was talking to Israel.
Then Samuel took a stone and set it up between Mizpah and Shen and
called its name Ebenezer; for he said, "till now the LORD has helped
Ebenezer is "Eben ha-`ezer" which means "stone of help." God was a rock of salvation to Israel; Samuel was setting up a monument of God's rock-ness (which is all throughout the bible) and salvation. God had, once again, helped Israel where they had messed up.
This is especially emphasized by the irony that "Ebenezer" was the name of the place that the Israelites had lost the ark to the Philistines. Aren't the literary connections in Scripture cool?
The first two lines in Come Thou Fount that contain Ebenezer go (at least according to The Trinity Hymnal)
Here I raise my Ebenezer; Hither by Thy help I'm come
The hymnist is, like Samuel, raising his stone of help as a tribute to God's salvation and grace. By thy help I've come this far; I praise you for it.
It's a great line because it captures the grace of God and the praise of Him for it in one succinct quote.