It was created to replicate/'come close to' the performance of the 125gr 357 magnum round that many agencies used in their revolvers. As they upgraded to semi-autos, they wanted more capacity with the same, proven round.

Many, many agencies use it today, for some of these reasons:
-The .357sig feeds great and by design will cycle w/o problems in most semi auto pistols.
-The .357sig offers a high level of KE and fast vel(fps) for it's size.
-The .357sig works a lot like the .40S&W or 9mmNATO and pistol magazines can hold 14-16 rounds. That could be a big + for a FAM or USSS special agent.
-The .357sig was available in the SIG P226/P229 platform which was already proven in military-US law enforcement circles.
-Large US law enforcement agencies like the Texas DPS, VA State Police and the DE State Police already picked & deployed SIG P226/P229 .357sig with great results. The DE State Police was the 1st major LE agency to use it.
-The .357sig in most duty rounds is accurate and offers great marksmanship.
-Top firearms/tactics instructor John Farnam, uses a .357sig in a DAK SIG Sauer. Other highly rated trainers carry or advocate the .357 sig too.

Probably the biggest factor that 'sold' the round to many agencies was its ability to penetrate barriers. Colorado SP used to use this round (may still) due to its 'fame' as a "truck stopper round".

CALIBERS -- 357SIG Advocacy

And in our own forum, this was already covered: What are the advantages of .357 SIG over .40 S&W?

Or just Google for it, especially look for the FBI ballistics data & pictures of penetration, wound channel, etc.

For me, I just like it... Since I reload, I can load up 357sig for next to nothing.