(edit 2: I wrote this late at night right before going to bed. Any oversights were not intentional but just a result of being very tired and trying to keep things short. Please see /u/EvanRWT's reply for additional information regarding the riots.)
The following is from a 1992 article in the New York Times from when it was happening:
In the South-Central area, where Korean shops have become the object of resentment even as they provide what is often the only retail service to residents
and
Lawrence Aubry, a member of the Los Angeles County Human Relations Commission, said Korean merchants had become a lightning rod for the discontent of some black residents. Many blacks in Los Angeles have remained poor as, one after another, immigrant groups have arrived and climbed past them to prosperity.
"It's illogical, but it's convenient to target the Koreans," he said.
It stands to reason that the Los Angeles County Human Relations Commission would have some idea about the situation, and his assessment can probably be taken as accurate for that reason.
Koreans has been moving into the area since the 1950s and there was a fair amount of resentment built up over the years. The situation was tense enough to motivate the creation of the Korean American Alliance, aka the Koreatown Immigrant Workers Alliance. The following is from their own website regarding the reasons for their creation:
KIWA was created in 1992 just two months before the Los Angeles Civil Unrest, often considered the nation’s first multi-racial riot. In a city torn with racism, poverty, and inequality, KIWA started with the mission to address the worker exploitation rampant in the Koreatown community among both Korean and Latino workers, and committed to struggling in solidarity with other communities for a more just Los Angeles for all.
(edit: As /u/CouldBeBetterForever and /u/ParkSungJun mentioned, the 1991 shooting of Latasha Harlins just a year before by a Korean shop owner was also a significant contributing factor to tensions between the two groups, which I should have mentioned initially but didn't. Thanks to them for the reminder.)
Of course, there have been other interpretations. One such example is from a 1998 study by Albert Bergesen and Max Herman (cited below) which suggests that the simple succession from one race to another is itself enough to foment rioting. That is to say that the very fact that there was such a succession would itself have pushed the community toward violence even in lieu of a flashpoint like the verdict. That said, there has been considerable sociological work on the topic of the 1992 riots specifically and on racial tensions in urban environments more generally which isn't really summarisable here.
tl;dr: Tensions has been rising between the different ethnic groups in the area for some time before the riots. The riots was just the point at which these tensions boiled over.
edit: There's also an interesting retrospective on blog.reuters.com, which includes video interviews, if you're interested in the history as well as how people dealt with it after the fact. It was a pretty major even (obviously) and it really extends well beyond April of that year.
This is a copy and past from a previous question about the asker's perception that other races have succeeded more than blacks. It's relevant because it touches on one of the underlying causes of tension between blacks and korean immigrants at the time.
If we are talking more recently then a big difference between blacks and other racial groups entering the US is that most did it by choice. It might have been a choice between coming to the US or starving in some cases, but they weren't severed from their previous life for generations against their will. Blacks were. Blacks had no connection with their former life, so they had no financial support, no one to write to for advice, no anything. If we take a more recent example from Korean-American immigrants they have a network of financial support and a strong sense of community. This was a contributing factor in the 1992 LA riots . People saw Koreans and other Asians moving into the area and buying businesses from locals and it caused a lot of tension. Koreans were borrowing money from other immigrants to get the money that banks wouldn't loan them. I'm not aware of any such support networks in black communities, which could lead to greater financial struggles which in turn could even increase poverty in black communities as other immigrants move into the businesses that would otherwise be run by black people.
There are other more immediate contributing factors that preceded the riots but I believe this is also relevant to the underlying tension.