In first-to-file systems, the filing date gives the owner priority right over anyone who files with an identical or a confusingly similar trademark after this date. Moreover, the owner of such a trademark can stop 3rd parties who merely use the brand name without holding any registration. Examples of countries that use this filing system are European Union, the UK, Germany, Japan and China.
Let's imagine a scenario where Marry uses her brand name in commerce. After a year, she decides to trademark it. In the first-to-file countries, she would be awarded the trademark rights if no identical or confusingly similar application was filed before hers.
On the other hand, based on the first-to-use system, the person who first used the mark in commerce, and can prove this, holds the right to the trademark. Countries that adhere to such filing rules are, for example, the US, Canada and Australia.
Let's use the same example as above. Marry has used her brand name in commerce for a year. She finds out her competitor, who started using the same name recently, has filed a trademark application in Australia. Mary will have legal grounds to stop such a person as she has used the trademark longer.