Convolutional neural network block notation
3x3 conv, 256, /2


stands for:


3x3 Kernel
256 filters
a stride of 2 halving the spatial dimensions


The latter is explained on page 3 where the authors state


  (ii) if the feature map size is halved, the number of filters is doubled so as to preserve the time complexity per layer. We perform downsampling directly by
  convolutional layers that have a stride of 2.


This means ResNet does, except for the beginning and end of the network, not use pooling layers to reduce spatial dimensions but conv. layers. 

Also, table 1 shows what is happening:



The part you have highlighted in your screenshot is the transition from conv3_x to the conv4_x layer of the 34-layer network. As you can see in the table the output size is reduced from 28x28 to 14x14 (that is what /2 does) while the filters are doubled from 128 to 256.