Most spells in Harry Potter (magic in general) are in Latin. However, at least two spells, namely Stupefy and Obliviate, are in English. Why is that? I found some sources, but they are in general talking about how magical language is Latin.
While RadarUnicorn is correct that spells such as Obliviate and Stupefy ARE pseudo-Latin just like other spells in the HP stories, there is at least one spell that seems to work with an English incantation:
Further reading (from a specialised sci-fi/fantasy site): What Wording Did Witches and Wizards in Other Cultures Use for Spells? and its many duplicates, as well as some of the answers to How could Ron possibly believe that “Sunshine, daisies, butter mellow…” is a real spell?
These spells are, like many other spells in Harry Potter, pseudo Latin.
Obliviate for example comes from the Latin word "oblivia" which means "forgetfulness".
The resemblance to English words is because English, like most European languages, has its roots in Latin.
This is just speculation on my part, but perhaps the language of the spell is representative of the nationality of the person who discovered/created it. I can't recall any mention of the origin of spells in the books.