An azimuth block mentioned in the software user guide is basically one column of the point cloud data - e.g. if you use mode 1024x10 it means that the data you are getting will be split into 1024 azimuth blocks, 64 points in each one (channel blocks), and they will be sent over ethernet in 1024 / 16 = 64 UDP packets. Each azimuth block has its Measurement ID that defines which column it is and therefore you can compute the azimuth of the column (in the lidar coordinate frame).
The channel blocks are the points in each column. It basically means each channel is a row of point cloud data. Both the OS1-16 and OS1-64 lidars always output 64 channels of data (64 samples in vertical field of view). If you are using the 16 channel version, you will find that most channels are always producing zeros because only 16 out of 64 channels are actually used. You have to refer to your documentation to find out which channels are used in your lidar unit because that can be configured (when buying the lidar). It can be set to uniform spacing or tighter spacing around horizon or below horizon (see Hardware User Guide, section 8 - Specifications, field of view)
For example, the lidar my company has uses uniform sampling where only the channel 2 and then every fourth channel are used for data. The left over space is not used and it is always set to zeros.