What are these red lights next to an airport runway?
These are VASI lights, which stands for Visual Approach Slope Indicator. When approaching a runway to land, an aircraft follows a specific glide slope. Usually, that slope is around -3 degrees. 

These VASI-lights help the pilot visually verifying that they are not too low and not too high. There are a total of four lights, representing two bars.

Now you only see two reds on the VASI, but there is also another color, that you will never get to see, except if you sit in a cockpit of a plane: White. Using this two colors, the VASI tells pilots if they are approaching the runway too high or too low.

The VASI works analog, so it does not know how high a plane is and it's position and changes lights accordingly. Both red and white light at the same time and by using a lens-mechanism, the pilots gets to see the correct lights.

There are three color codes of a VASI:



Source

When both the VASI-bars are red, as in your picture, the plane is too low and needs to pitch up. Red and white means on glidepath and two whites mean too high and the pilot needs to descend faster.

There's also a mnemonic to remember the (very easy tbh) color codes:


  White over White, you're high as a kite.
  
  Red over White, you're alright.
  
  Red over Red, you're dead. 
  
  White over Red, unsaid.


(White over red is no color code actually, because you would have to fly inverted to get it, that's why it's "unsaid". 

Here's how a VASI-light looks close-up:



Source