‘Holy’ and ‘sanctify’ are closely related words. To ‘sanctify’ something means to ‘make it holy’ — i.e. ‘sanctification’ is the “process” whereby something goes from being unholy to holy.
In fact, sometimes Bible translators use the phrase ‘made it holy’ (or similar) instead of ‘sanctified’; compare, for example, the following two Old Testament verses that translate the same Hebrew word (often usually translated as ‘sanctified’) differently:
For in six days the Lord made heaven and earth, the sea, and all that is in them, and rested the seventh day. Therefore the Lord blessed the Sabbath day and made it holy [Heb. qadash; Strong’s #6942]. (Ex. 20:11)
When I bring them back from the peoples and gather them from the lands of their enemies, then I shall be sanctified [Heb. qadash; Strong’s #6942] through them in the sight of the many nations. (Ezek. 39:27, NASB)
The connection between ‘holy’ and ‘sanctified’ can be seen quite well in Ezek. 39. Here God repeatedly declares that he is holy (Ezek. 39:7,25); he then says that the day is coming when other nations, as well as Israel, will consider him as holy (Ezek. 39:27, quoted above). The other nations previously didn’t count God as holy, but their opinion will change, and thus what wasn’t holy to them will become holy to them, will be sanctified.