What does « Trace / Vestige » mean in the Quran?

He said, "They are close upon my tracks, and I hastened to You, my Lord, that You be pleased."

He said, "I saw what they did not see, so I took a handful [of dust] from the track of the messenger and threw it, and thus did my soul entice me."

So observe the effects of the mercy of Allah - how He gives life to the earth after its lifelessness. Indeed, that [same one] will give life to the dead, and He is over all things competent.

Indeed, it is We who bring the dead to life and record what they have put forth and what they left behind, and all things We have enumerated in a clear register.

So they hastened [to follow] in their footsteps.

Have they not traveled through the land and observed how was the end of those who were before them? They were greater than them in strength and in impression on the land, but Allah seized them for their sins. And they had not from Allah any protector.

Have they not traveled through the land and observed how was the end of those before them? They were more numerous than themselves and greater in strength and in impression on the land, but they were not availed by what they used to earn.

Rather, they say, "Indeed, we found our fathers upon a religion, and we are in their footsteps [rightly] guided."

And similarly, We did not send before you any warner into a city except that its affluent said, "Indeed, we found our fathers upon a religion, and we are, in their footsteps, following."

Say, [O Muhammad], "Have you considered that which you invoke besides Allah? Show me what they have created of the earth; or did they have partnership in [creation of] the heavens? Bring me a scripture [revealed] before this or a [remaining] trace of knowledge, if you should be truthful."

Muhammad is the Messenger of Allah; and those with him are forceful against the disbelievers, merciful among themselves. You see them bowing and prostrating [in prayer], seeking bounty from Allah and [His] pleasure. Their mark is on their faces from the trace of prostration. That is their description in the Torah. And their description in the Gospel is as a plant which produces its offshoots and strengthens them so they grow firm and stand upon their stalks, delighting the sowers - so that Allah may enrage by them the disbelievers. Allah has promised those who believe and do righteous deeds among them forgiveness and a great reward.

Then We sent following their footsteps Our messengers and followed [them] with Jesus, the son of Mary, and gave him the Gospel. And We placed in the hearts of those who followed him compassion and mercy and monasticism, which they innovated; We did not prescribe it for them except [that they did so] seeking the approval of Allah. But they did not observe it with due observance. So We gave the ones who believed among them their reward, but many of them are defiantly disobedient.

And [also for] those who were settled in al-Madinah and [adopted] the faith before them. They love those who emigrated to them and find not any want in their breasts of what the emigrants were given but give [them] preference over themselves, even though they are in privation. And whoever is protected from the stinginess of his soul - it is those who will be the successful.

And said, "This is not but magic imitated [from others].

And preferred the life of the world,

But you prefer the worldly life,