What does Acts 13:48 mean which is often quoted by Calvinists?

Acts 13:48  And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.

Yeah, what I think it means is that the gentiles who were appointed by God for eternal life believed, and the others didn't. Ok, I am not helping much am I? : ) What I am saying is that just take it as the verse says. There are several verses that say similar things. The reality is that without the work of God none would be saved. Jesus was clear that: 

Joh 6:44  No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day.

This is clear and true for every salvation without exceptions. Paul was equally clear about the election and choosing of God of believers:

Eph 1:4-5  For he chose us in him before the creation of the world to be holy and blameless in his sight. In love  (5)  he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will

So what does that mean? That Calvinists are correct? No. I am no great fan of Calvinism as it is 'one-sided theology'. That is, I believe it focuses on some scriptures and leaves out others which are equally clear that 'whosoever wills may come'. For example:

Joh 3:16  "For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life.
John 7:17 “Anyone who chooses to do the will of God will find out whether my teaching comes from God or whether I speak on my own.”
Rom 10:13  For "whoever calls on the name of the Lord shall be saved."
Rev 22:17  And the Spirit and the bride say, "Come!" And let him who hears say, "Come!" And let him who thirsts come. Whoever desires, let him take the water of life freely.

And that free will to receive the Lord is, as we see greatly, also there to reject Him. Jesus longed for the people of Jerusalem but mourned over the state of their hearts for they were NOT WILLING to receive Him:

Mat 23:37-39  O Jerusalem, Jerusalem, you who kill the prophets and stone those sent to you, how often I have longed to gather your children together, as a hen gathers her chicks under her wings, but you were not willing.  (38)  Look, your house is left to you desolate.  (39)  For I tell you, you will not see me again until you say, 'Blessed is he who comes in the name of the Lord.' "

So we see both sides. We see that Jesus said that no one can come to Him without the Father drawing them. And we also see Him sorrowful that the people were not willing to accept Him. We have to hold to both.
Getting back to Acts 13:48, William MacDonald writes well in the Believers Bible Commentary:

"All who were appointed to eternal life believed. This verse is a simple statement of the sovereign election of God. It should be taken at its face value and believed. The Bible teaches definitely that God chose some before the foundation of the world to be in Christ. It teaches with equal emphasis that man is a free moral agent and that if he will accept Jesus Christ as Lord and Savior, he will be saved. Divine election and human responsibility are both scriptural truths, and neither should be emphasized at the expense of the other. While there seems to be a conflict between the two, this conflict exists only in the human mind, and not in the mind of God."

The Bible does speak of predestination and God's choice/election. But we should also bear in mind that it often does so in connection to the foreknowledge of God:

Rom 8:29  For those God foreknew he also predestined to be conformed to the likeness of his Son, that he might be the firstborn among many brothers.
1Pe 1:2  who have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, for obedience to Jesus Christ and sprinkling by his blood: Grace and peace be yours in abundance.

The fact is that any 'choice' that is made, whether by God or man, is based upon knowledge. For you and me, that is more than a little limited at times and we may make poor decisions. But God knows all things, even before they came into being. All things... for all time. So every choice He makes is based on perfect knowledge and understanding. For example, He chose Jeremiah to be His prophet. And when did He do that? Even before Jeremiah was born! 

Jer 1:5  Before I formed you in the womb I knew you, before you were born I set you apart; I appointed you as a prophet to the nations.

In fact God even says that He 'knew' Jeremiah before He formed Him in the womb. How? Because He foreknew His entire life, character, heart and ministry... and all of that knowledge came into His choice of Jeremiah.

So yes, there is always going to be a mystery here but we leave this with God and teach what the Bible teaches - even if it seems hard to reconcile with another scripture. What we don't do is go to 'one-sided theology' and only focus on one side of the scriptures while leaving the others out. I have written about this a little before. Have a look here:

https://jesusplusnothing.com/series/post/freewillelection

And please read this excellent short article on "one-sided theology' by C.H.M here:

https://www.stempublishing.com/authors/mackintosh/Bk6/ONESIDED.html

Hope this helps.

Iain.