Is it necessary to play Dark Souls I / II before I play III?
No, it's not necessary. You are able to complete DS3 and understand it till some point without any background in series.
But experience with previous games will help you:
- in understanding basic game mechanics like bonfires, weapon scaling and movesets, etc.
- in understanding the entire story: while each game have independent plot, there are a lot of interceptions. In terms of lore games complete each other.
Also, some things in DS3 could be considered as pure fan-service related to previous games, so without knowledge of first two you could barely notice these things at all. But this no way spoils your experience with the game.
Dark Souls is a great series, I hope you will enjoy it.
The short version is no, you really don't. The souls titles are all variations on a theme and not a continuous narrative. You will not understand the lore / story your first time through anyway so you shouldn't worry about that.
The slightly lengthy answer is that you can skip 2, its a great game I enjoyed it but it doesn't really add much to 3. Whether you should play 1 isn't really an easy question to answer. Many people would say absolutely but one thing to bare in mind is that these are polarizing games, and what makes 1 so brilliant is also what makes it so challenging to get in to.
I don't mean challenging from a combat perspective either, but from a world and level design perspective Dark Souls 1 is brutal and while it does make the whole world feel whole, 3 does almost as good a job and is way less isolating. Some would disagree but as I said, its polarizing.
Dark Souls 3 does have a lot of throw backs to 1, and some for 2 but these aren't reasons to play, they aren't going to blow you away unless you've already invested a lot into the game and its lore.
For me 3 is the pinnacle of the series, where it refined what was great, made it more accessible but at didn't skimp on the challenge. What makes them great is how they make you feel as a player, not the lore of the story behind it all.
No you don't need to play the others games to understand the game.