I guess you are talking about either the smallpox vaccination or the TB vaccination, since most other vaccines don't leave a mark.
For the smallpox vaccination, "leaving a mark" is the sign that the vaccine worked. The vaccine requires multiple punctures giving multiple infection start sites, so it becomes very inflammatory - leaving behind the scar tissue. The TB vaccine is different, in that it is a single injection, but BCG is extremely immunogenic and causes severe local inflammation, which can cause a long-lasting scar.
As to why you see it on some people and not others:
* Neither vaccine is ubiquitous anymore. With smallpox now gone, very people are currently vaccinated. TB is still a major problem, but vaccination depends on the region. In Europe, for example, you will see very few vaccination scars.
* Not everyone is vaccinated on the arm. Some local authorities vaccinate on the bottom, for example.
* Different people react differently to scars in general, not just vaccine scars. This depends on the amount of fibrosis (more fibrosis gives more prominent scars which can become more obvious with age) and external factors (exposure to sunlight, etc).
But if persons with out this mark indicate that the vaccine didnot actually work in them. More over in some persons the marks grows as they become old to certain point, where as in others it will remain same..