These options let you configure the way PuTTY keeps text after it scrolls off the top of the screen (see section 3.1.2).
The ‘Lines of scrollback’ box lets you configure how many lines of text PuTTY keeps. The ‘Display scrollbar’ options allow you to hide the scrollbar (although you can still view the scrollback using the keyboard as described in section 3.1.2). You can separately configure whether the scrollbar is shown in full-screen mode and in normal modes.
If you are viewing part of the scrollback when the server sends more text to PuTTY, the screen will revert to showing the current terminal contents. You can disable this behaviour by turning off ‘Reset scrollback on display activity’. You can also make the screen revert when you press a key, by turning on ‘Reset scrollback on keypress’.