Everyone refers to all the members of a group of people. Every one refers to each member of a group of items or people considered individually.
Everyone arrived at the meeting on time.
We thought we would have enough glassware to run the experiment tomorrow, but it turns out that every one of the flasks is cracked.
We invited six well-known toxicologists to our seminar, but every one turned down our invitation.
See also everybody/every body and anyone/any one.