Welch World is a nickname adopt by certain Black Disciples in Chicago as an honor for one of their fallen members, Anthony Welch. Welch was murdered by a hail of gunfire on the night of May 15, 2010. Following Welch's death, Welch World was created as a tribute.
It's very common for gang members in Chicago to adopt nicknames for fallen gang members. Welch World itself started becoming popular due to the spread of Drill music which is dominated by gang members whom often reference their gangs in songs. Billionaire Black whom is from Welch World often reference it in his songs, such as in "I Can't Help It" in which he says "n*gga I'm the sh*t like I live in the sewer, Welch World Wayne, f*ck n*gga thats my shooter". Lil Jay also made a reference to Welch World in his song "How U Aint No" in which he said "How U ain't no it's Welch World and Tookaville", this line was a reference to Billionaire's gang and Lil Jay's gang(STL/Tookaville).