Question: So... I just got Hitman: Absolution for PS3. I have started playing a few missions, but I feel like I am missing something.

Do I feel like I am missing something because I haven't played the other Hitman games OR of my failure to understand the story due to some other reason?

**Should I play the other Hitman games to understand the story?**

Answer: 
This answer may be different for everyone but I am going to say no. After you finish absolution, a lot of your questions will be answered [ I'm not going to provide those spoilers]. If you want some Hitman Lore, check out this very short video explaining some background to Agent 47
Not really, but i do recommend you do play the other ones :)