Three area codes were originally assigned to different regions of California in 1947. Area code 213 is one of them - remaining two area codes are 415 and 916. It was associated with Los Angeles at the time of its creation as it was covering Southern California completely at that time.
With passage of time - increase in population and technology advancements amplified the demands of people. There was time when people were satisfied by having just one telephone connection at a time but now they need separate phone lines for internet and telephone as they don't want any kind of interuption in any service.
Such amplification of phone connections made it essential to divide the regions into parts and assign different codes to each divided part. Codes are assigned to areas to uniquely identify them - making it essential to dial code of the area even while making local calls.
This is why area 213 has been further divided so many times till now. As a result area covered by code 213 reduced to area of downtown Los Angeles only. Besides that, area code 323 completely surrounds the areas of code 213. Other area codes covering certain parts of Southern California are: