Bulb C gets brighter. When B is connected in parallel with A the total resistance of the circuit decreases and a larger current flows from the power supply. Since all of the power supply current passes through C it gets brighter when this current increases.
Bulb A gets dimmer. Bulbs A and B split the power supply current between them after B is connected: each gets half. Although the total power supply current increases when B is connected, it does not double because the total resistance of the circuit includes A and B in parallel but C in series. So A and B each carry a smaller current than A alone did. Thus they are dimmer.
Note the bulbs are suitable only for qualitative work. Quantitative work is complicated by the fact that the resistance of the bulbs increases with increasing current (the filament gets quite hot, hot enough to glow).