The positive sign for the a path means that $X$ is positively associated with $M$, and the negative sign for the b path merely means that $M$ is negatively associated with $Y$ (as $M$ increases, $Y$ tends to decrease). In other words, increases in $X$ predict increases in $M$, which, in turn, predict decreases in $Y$. The significant mediation indicates that part of the statistical association between $X$ and $Y$ is transmitted indirectly through changes in $M$, regardless of the specific sign for the a and b paths.
I'm not familiar with the term "competitive mediation". However, it seems to refer to the fact that the direct effect of $X$ on $Y$ is positive, whereas the mediation model suggests that increases in $X$ are indirectly associated with decreases in $Y$, through increases in $M$.