Half-life, more technically, is the period of time in which any one atom of the substance has a 50% chance of decaying.
As it happens, when dealing with large quantities of a substance (and any quantity of atoms you can weigh is 'large'), this means that pretty much exactly[1] half of it decays in that period of time.
If your isotope X had a half life of 1 day, and you had one atom, after 1 day there is a 50% chance it would be gone.
After 10 days there would be a (1-2^-10)*100% chance it would be gone, or about 99.9% chance.
There would never be a 100% chance it was gone.
Interestingly, even protons have a half life. There is a period far far far far[2] in the future when there is a greater than 50% chance that every proton in the universe will have decayed, assuming something else catastrophic doesn't happen first.
Footnotes:
[1]: Basically, the odds that >51% or <49% would be left are on the same order of magnitude as the atoms in your room spontaniously assembling into a working computer. Well, not quite... =)
[2]: No, I actually didn't use enough "far"s.
Not by a long shot.