This is the game part where you can check your standing in the charts, or your bands', or recordings' of your bands. You can find it in top menu.
The first Charts page shows the current leaders of charts. Only the top 3 are shown. For a more detailed information you will have to go to corresponding page.
The Singles chart page shows all currently charting songs. You can overview some information of the song like position, name, the band, that recorded this single, the position from last turn, highest position and how many turns this song is charting.
The Albums chart page shows all currently charting albums. Similarly to singles charts, you can observe position, name, the band, that recorded this album, the position from last turn, highest position and how many turns this album is charting.
The Bands chart page shows the standing of all bands, that were not disbanded. You can check information like position, name, the manager (the owner of the band), the position from last turn, highest position, fame and rating. The position of the band is determined by the sum of rating and fame of it's recordings, and the fame of the band itself. The recording's contribution to band's rating depends on it's age. The recording, that was created in the last 3 months, will add 2x of it's rating and fame, from 3 to 6 months ago created recordings will add 1x, from 6 to 9 months - will add 0.5x, and older than 9 months recordings will not be included in calculating band's rating. The fame of the band is also constantly changing. Every turn the band lose some fame. But it can regain it by releasing songs and albums, because every band gets fame from charting recordings. The promoting and gigging instructions also adds fame.
The Managers chart page shows the standing of all managers. You can observe information like position, name, the position from last turn, highest position, rating and money. The position of the manager is determined by it's rating, which is the sum of it's bands' ratings, the amount of money, studio and shop vault upgrade bonus, and shop items. Because band's rating is constantly changing, so does manager's rating. So keep an eye on what your bands are doing, otherwise you could slip down in managers chart.