What is meant by a programmble PWM controller IC?
Is it programmable means writing code or by connecting external resistor to the particular pin to achieve?

 

Why not give us the link to the datasheet ?

Programmable means a lot of things, typically the setting of registers internal to the IC or using passives externally to alter its functionality.

Steve

 

LM5021 is the IC

 

"Single Resistor Programmable Oscillator" from the datasheet should be pretty clear.
You may control the frequency of operation via a single resistor connected to the IC.

Steve

 

what are all the criteria to choose a PWM Controller IC?

 

Your questions are too general, you need to 'brush up' on what you are doing and, if you get stuck, then ask for help. And consider thanking people for their valuable time.

Steve