Below is a short description about each button.

Bold text icon Bold text style (Ctrl+B).
Italic text icon Italic text style (Ctrl+I).
Underline text icon. Underline text style (Ctrl+U).
Strikethrough text icon. Strikethrough text style.
Align left icon. Align left.
Align center icon. Align center.
Align right icon. Align right.
Align full icon. Align full.
Unordered list/bullet list icon. Unordered list/bullet list.
Ordered list/numbered list icon. Ordered list/numbered list
Outdent/decrease indentation icon. Outdent/decrease indentation.
Indent/increase indentation icon. Indent/increase indentation.
Undo the last operation. Undo the last operation (Ctrl+Z).
Redo the last operation icon. Redo the last operation (Ctrl+Y).
Insert a new link icon. Insert a new link, read more about this function in the Insert link section.
Unlinks the current selection icon. Unlinks the current selection/removes all selected links.
Insert a new anchor icon. Insert a new anchor, read more about this function in the Insert anchor section.
Insert a new image icon. Insert a new image, read more about this function in the Insert image section.
Cleanup code icon. Cleanup code/Removes unwanted formating. This function is useful when you copy contents from for example a office product.
Show help icon. Shows this help window.
Source code editor icon. Opens HTML source code editor.
Insert table icon. Inserts a new table at the current location.
Adds a row above icon. Adds a row above the current one.
Adds a row under icon. Adds a row under the current one.
Remove row icon. Removes the row.
Add column before icon. Adds a column before the current one.
Add column after icon. Adds a column after the current one.
Remove column icon. Removes the current column.
Insert horizontal ruler icon. Inserts a new horizontal ruler
Remove formatting icon. Removes formatting from the selection.
Subscript icon. Makes the selection to be subscript.
Superscript icon. Makes the selection to be superscripted.