I don't know how to explain but it is about limiting audio
The second one looks hella clipped, isn't it distorting? 

Anyway the effect you're after is unsurprisingly called a limiter. A limiter is a form of compressor, so a compressor can also be used, by setting the compression ratio high. 

Premiere ships with a filter called hard limiter, and a compressor as well, but there are plenty more free and commercial VST limiter plugins out there, and scads of compressors if you want more knobs to twiddle.