The meaning of "particular" in this case means: "Separate and distinct from others of the same group, category, or nature", American Heritage Dictionary. In application to the Particular Baptists, this means we believe the Scriptures teach that God elected, chose, a particular people for His own and gave them to the Son. The Son came to save these particular people so his blood was shed for these particular people, not all or a general redemption. Why do "I" believe this? I share just a couple of many verses I find that drive me to that belief.
“When the Gentiles heard this, they were glad and praised the word of the Lord; and as many as had been destined for eternal life became believers.” (Ac 13:48 NRSV)
“When the Gentiles heard this, they were very glad and thanked the Lord for his message; and all who were chosen for eternal life became believers.” (Ac 13:48 NLT)
“the Gentiles listened with delight and extolled the lord’s message; and all who were pre-destined to the life of the ages believed.” (Ac 13:48 WEY)
So, a "particular" people for the Son had been chosen, destined, predestined to become believers and thus saints of God. Other translations have "appointed" or "ordained". So, of those predestined, ordained, chose; he came to shed His blood for them.
“... for thou wast slain, and hast redeemed us to God by thy blood out of every kindred, and tongue, and people, and nation;” (Re 5:9 AV)
“... because thou hast been offered in sacrifice, and hast purchased for god with thine own blood some out of every tribe and language and people and nation,” (Re 5:9 WEY)
"... because thou wast slain, and didst redeem us to God in thy blood, out of every tribe, and tongue, and people, and nation,” (Re 5:9 YLT)
It is quite clear to me, God chose a "particular" number of people and the Son saved these people, the elect, and none other. I have no idea who the elect are, they are those who God wrote into the book of life from before creation and at God's time will receive the grace of faith.
“The beast that you saw was, and is not, and is about to rise from the bottomless pit and go to destruction. And the dwellers on earth whose names have not been written in the book of life from the foundation of the world will marvel to see the beast, because it was and is not and is to come.” (Re 17:8 ESV)
“I am the good shepherd. I know my own and my own know me, just as the Father knows me and I know the Father; and I lay down my life for the sheep. And I have other sheep that are not of this fold. I must bring them also, and they will listen to my voice. So there will be one flock, one shepherd.” (Joh 10:14-16 ESV)
I find that particularism gives ALL glory and honor to God, not to man's believing, because faith is God's gift to his chosen ones, the elect. God foreknew those persons to whom he was going to give the gift of faith, his chosen ones, the elect.
May God open our minds and bless us with his truth.