what this part does? 16116759836

I know where it located,but i can't figure it out what it does in term sending fuel from where to where? What does keep the fuel pressure in fuel line after car is off ?. I have first poor start in the morning. it starts right the way but RMP goes up to 1000. When i start 2 time it jump to 1200-1300 with powerful start and then go to 600 right the way. All new filter, pump good gas always 93. Thank you guys for any suggestions.