Transforming NFA into DFA
This is the standard procedure for converting NFAs to DFAs. The first row should be read as "If you know you're in one of the states $0$, $1$ and $4$ and you read an $a$, you'll have to be in one of the states $1$, $2$ and $4$; if you read a $b$, you'll have to be in one of $1$, $4$ and $5$." The other rows are similar.