What you are seeing is most likely a visual approach aid.
You described two types: VASI and PAPI.
PAPI, or Precision Approach Path Indicator lights, consist of four lights. If all four are white, you are high (generally on a typical runway, on a glidepath steeper than 3.5 degrees). If you see one red and three white, you are slightly high (average around 3.2 degrees). Two red and two white indicate you are on glidepath, roughly 3 degrees for most runways. Three red and one white mean you are slightly low (around 2.8 degrees typically), and four red mean you're quite low (less than 2.5 degree glidepath.)
VASI, or Visual Approach Slope Indicator, is the other kind you described.
The "two-by-two" configuration you mentioned is called a two-bar VASI and is the most typical installation that I've seen. Bars can be either red or white. Basically, a red bar indicates that you will touch down before you reach the bar; a white bar means you will touch down past it.
If the near bar is white and the far bar is red, you are on glidepath. If both bars are white, you are above glidepath. And, if both are red, you're below glidepath.
The easiest way to remember this is: Red over white, you're all right. Red over red...well....you're dead.