Race Comment Explainer

Original comment with matches highlighted:

held up towards rear, untidy 3rd, on inside 6th, pushed along 2 out,

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.
home turn	This is the final bend or corner of the track, just before the horses enter the final straight run to the finish line.
No extra	Did not improve or accelerate when asked.
Held up	Intentionally raced patiently at the back to save energy.
Headway	The horse was moving up through the field.

Summary

The jockey started to urge the horse (hand-riding, not necessarily using the whip).
Running near the back of the field.
This is the final bend or corner of the track, just before the horses enter the final straight run to the finish line.
Did not improve or accelerate when asked.
Intentionally raced patiently at the back to save energy.
The horse was moving up through the field.