Filters are used to remove unwanted data from the pivot chart. You can use filters in the pivot chart or in the corresponding pivot table, since the resulting chart is exactly the same.
Pivot chart buttons are unique to pivot charts, normal charts don't have them. The buttons shows the layout of the pivot table, which are the pivot table fields. If present, page fields are displayed in the top. Row fields are displayed on the bottom of the chart next to each other and the legend shows the buttons from column fields stacked.
The buttons have a pop-up action attached to them. If there is some filtering applied, then the arrow turns blue (similar to the pivot table), so it is easier to see when a field has any filter applied.
Existing page fields shows what is filtered: when nothing is filtered "- all -" is shown, when some data is filtered, then "- multiple -" is shown and when only one value is not filtered, the value is shown.