Impost
Weight carried or assigned.  

In Hand
Running under moderate control, at less than top speed.  

In The Money
A horse that finishes first, second or third.  

Infield
 Area encompassed by the inner rail of the racetrack.

Inquiry
Reviewing the race to check into a possible infraction of the rules. Also, a sign flashed by officials on the tote board on such occasions. If lodged by a jockey, it is called an objection.  

Isolation Barn
A facility used to separate sick horses from healthy ones.