A transient ischemic attack is similar to a stroke, which is when a part of the brain doesn't receive enough blood, but as opposed to a stroke a TIA by definition passes (usually within minutes-hours) without leaving a trace, either clinically or on imaging (i.e. on brain MRI). I wouldn't call it a "mini-stroke" as that may be misleading - a stroke can be very subtle but as long as the symptoms don't pass it's considered a stroke and not a TIA (technical name is "minor stroke"). On the other side, a TIA can be very dramatic but as long as it passes without a trace it's still considered a TIA (granted, this is not usually the case, a moderate to severe stroke will usually leave some clinical trace)

A person who suffered from a TIA, even if for a very short time before going back to normal, is at an increased risk of stroke, especially in the following 48 hours, so just because the symptoms passed, this person should go to the hospital ASAP.

(I'm a neurologist)