Race Comment Explainer

Original comment with matches highlighted:

towards rear, pushed along 3f out, ridden and approaching final ,

Matched phrases & meanings

Phrase	Meaning
Pushed along	The jockey started to urge the horse (hand-riding, not necessarily using the whip).
Towards rear	Running near the back of the field.
Furlong	Unit of distance; one furlong is 1/8 of a mile (approx. 200 meters).
Headway	The horse was moving up through the field.
Ran on	The horse maintained or increased its speed in the final stages.

Summary

The jockey started to urge the horse (hand-riding, not necessarily using the whip).
Running near the back of the field.
Unit of distance; one furlong is 1/8 of a mile (approx. 200 meters).
The horse was moving up through the field.
The horse maintained or increased its speed in the final stages.