"But I tell you, love your enemies and pray for those who persecute you, that you may be children of your Father in heaven. He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous." - Matthew 5:44-45
basically it means to harm people for their belief
it likely was used to mean "imprison people for their beliefs" at the time but nowadays it's been reduced to simple mockery or jeering (which is also described as persecution but is used as a separate word)
when it was written people were thrown in jail for falling out of line with whatever the government believed
so if you were in Rome, you got arrested for not praising the roman gods and if you were Jewish you might get arrested for believing in Christ