Asset swap spread is like trading cards.
Let's pretend you have a Lionel Messi card and a Neymar card. You love Messi but you think Neymar is okay, so you trade the Neymar card for a better Messi card.
The asset swap spread works the same way but instead of trading cards, people trade bonds. A bond is just an agreement where someone loans money and promises to pay it back with interest down the road.
Two people might look at a certain bond and think it's worth different amounts. One person might think it's worth more than the other person does. So, they can trade it. The person who thinks it's worth less can trade it for another bond they think is worth more.
The asset swap spread is the difference between the bond they are selling and the bond they are buying. The bigger the difference, the better the trade for one of the people.
Just like how some people like Messi more than Neymar, some people like certain bonds more than others, so they are willing to trade to get the bond they prefer.