That's that thing they put in single records so they could play in a turntable, right?

This is for 45s so that they can be played.

You're both right! RCA started selling the smaller, 45 RPM records with bigger holes. But most people had the record player with the smaller spindle. Thus the need for the adapter... But why the change? Let's turn to RCA Review and the June 1949 article explaining it:

All record changers require a selecting mechanism of some sort to separate individual records from the stack. With records of constant thickness, all practical designs of selecting means cause some damage to the edge, body, or center hole area since the records have to be forced apart or slid one against the other to effect selection. With a small center hole and the heavy records commonly used, high stresses occur around the center hole and record damage results. A small center hole does not permit record stability on the spindle without edge support or complex spindle mechanism. Further, the small hole makes loading difficult.

The necessity of accommodating records of two diameters brings about record changer complexity and customer inconvenience. The very magnitude of the diameters makes the record changing mechanism big. Cabinets to accommodate such record changers and also provide record storage become large and therefore expensive. The relatively high rotational speed of the turntable necessitates the use of speed reducing mechanism to give the record changer time to perform its several functions reliably.

DETERMINATION OF THE RECORD CHANGER DESIGN

The solution to these problems, when considered against the ideal of minimum space requirements, minimum cost, maximum performance, and maximum convenience of customer operation, dictated a major change from existing practice. After study of the problem, it was concluded that a simple record changer design could be accomplished if the following conditions were satisfied:

1. A large center spindle housing the separating means. It was found that a 1-1/2-inch diameter spindle would house an economical selecting mechanism, provide adequate record stability on the spindle without external support, and make for easy loading of records on the spindle.