According to 23andme's Twitter
Approximately 8% of DNA is originally from viruses, which infected your ancestors and became integrated into their cells.
Normal viruses infect cells in order to take advantage of cellular mechanisms to reproduce themselves. A class of viruses known as "retroviruses" have a slightly peculiar mechanism to achieve this - they synthesise a special enzyme called "reverse transcriptase", which translates their own RNA into DNA which is incorporated into the host cell's genome. The host cell then replicates the virus' DNA alongside the rest of its own.
Should a retrovirus happen to infect a germ line cell - i.e., a sperm or an ovum - the retroviral DNA will be copied into the offspring's DNA. And their offspring. That's called an "endogenous retrovirus". Some cause or contribute to cancers - and sometimes (for example) that DNA even gets co-opted for a useful purpose.
Given thousands or millions of generations, these endogenous infections accumulate. It doesn't even have to be independent infections - when a cell is infected it produces new copies of the RNA virus which can insert itself again somewhere else in the germline genome - even across the generations. They eventually tend to get deactivated by one mutation or another, but phylogenetic studies have shown that the some 98,000 retroviral elements and fragments in the human genome come from relatively few infections.
Estimates vary - many of the retroviral sequences have been modified by mutation over the aeons, making it hard to find them all - but recent estimates do come to about 8% of the human genome having a retroviral origin. There's a fair chunk of virus in all of us.