I appreciate it can be a worry undergoing tests but please don't over think your situation for now.
The important thing to remember is that cervical screening is all about prevention. It is designed to pick up abnormality that can be monitored or treated to prevent cervical cancer.
Whilst HPV is usually cleared by the body's immune system within a couple of years in some people it can persist for much longer. This is more likely to happen in smokers or in people who have a weakened immune system.
HPV on it's own is a very common virus and most sexually active people will come into contact with it at some point in their life without it causing problems.
In recent years it has been found that high risk strains of HPV is responsible for most abnormal cells in the cervix which is why the cervical screening programme now checks for this as the first test. Then the sample is then closely examined for cell changes that if left could eventually turn into cancer over time. If the sample only reveals normal cells this is reassuring and that person is checked out a year later.
As in your case where someone has 3 HPV positive screening results then it is just protocol at this point to be invited to colposcopy for a review of the cervix. It really doesn't mean anything serious is going on, so try not to worry.
At your appointment the colposcopist will explain what needs to happen at the time and any follow up appointments according to their assessment.
