Andrew makes a number of good points about this chart. Make sure you read the whole post.
One of his points concerns making the line smoother by removing the within-week fluctuations. Doing so removes the weekday/weekend effect. By removing effects that are not of interest, we can focus on effects that are interesting. The number of births on any given day is a confluence of many factors, weekday/weekend being one of them. If we don't remove some of the contributing factors, we'd have no idea which factors are more important and which are less so.
The problem of "confounding" in complex datasets is demonstrated in the heat map, which Gelman also cited, without approval:
The weakness of heat maps is the reliance on color scales. Most software does not allow precise mapping of numbers to colors. The color pattern is automatically generated, which is often not to our liking. Even if the colors are acceptable, it is impossible to learn anything from a heat map other than the big-picture patterns.
The big-picture pattern we find here includes summer months being most popular for births while springtime is less popular. I fail to find any consistent patterns in the rows. If this is the key message, then we can collapse the rows, and even collapse the columns into seasons.
But what is the color scale? The colors correspond to ranks. Ranks ignore the actual difference between two data points. In other words, all the drastic troughs and peaks in the line chart disappear from this heat map. There are much better ways to turn count data into discrete bins.
Picking the right ranking scheme is the most pressing issue here. The designer ranks all 366 days in one overall ranking. This ranking serves to play up the summer bulge in births but obscures other patterns.
Alternatively, days can be ranked within each month. That would remove the month-to-month effect and highlight the day-of-the-month effect.