Adding a relay to the starting system ensures full battery voltage is being applied to the starter solenoid so it can energize as designed. Normally, source voltage is supplied by the ignition switch via the yellow wire. However, along with a borderline battery (or not), there could be voltage drop caused by oxidized/loose connections/contact points in the fuse box, switch, circuit and/or the longish 8-9' path from switch to solenoid.
Installing a relay closer to the starter results in a shorter path for the "yellow" wire. Voltage source is now via the battery cable that also powers the starter motor.
Hope this helps,
Sherwood
FWIW,
Remote Starter