Why A link budget adds up transmit power plus antenna gains minus all the losses (feed line, path loss, pointing, atmospheric) to predict how much signal actually arrives at the receiver input. Link margin is what is left over: the received power level minus the minimum signal level the receiver needs to decode the signal, expressed in dB. A positive margin means the link works and has some reserve for fading; a margin near zero means any fade drops you below threshold.
Watch out Transmit power minus receiver sensitivity ignores every gain and loss between the two ends, which is the whole point of the link budget calculation. Fade margin is essentially the same idea as reserve above threshold, not the opposite of link margin.
Margin = what you get minus what you need, in dB. Positive margin means the link closes.