There are several resources for learning about HDF5. The HDF Group provides an on-line HDF5 tutorial, documentation, examples, and videos. There are also tutorials provided by other organizations that are very useful for learning about HDF5.

The HDF Group

For a quick introduction to HDF5 see the following:

Introduction to HDF5A very brief introduction to HDF5 and the HDF5 programming model and APIs
Learning HDF5 with HDFViewA tutorial for learning how to use HDFView. NO programming involved!
Learning the BasicsStep by step instructions for learning HDF5 that include programming examples

 

These tutorials and examples are available for learning about the HDF5 High Level APIs, tools, Parallel HDF5, and the HDF5-1.10 VDS and SWMR new features:

Using the High Level APIsH5LT (Lite)    H5IM (Image)    H5TB (Table)    H5PT (Packet Table)    H5DS (Dimension Scale)
Introduction to Parallel HDF5A brief introduction to Parallel HDF5. If you are new to HDF5 please see the Learning the Basics topic first. 
Tools for Viewing and Editing HDF5 Files:

Learning HDF5 with HDFView

Using the HDF5 Command-line Tools

Use Case - JPSS NPP Files
HDF5-1.10 New Features

Introduction to the Virtual Dataset - VDS    

Introduction to Single-Writer/Multiple-Reader (SWMR)
Example Programs  
VideosIntroduction to HDF5
Parallel HDF5

 

For more information, see the HDF5 User's Guide, Reference Manual and other documentation.

Other

NEON (National Ecological Observatory Network) HDF5 Tutorials

NERSC Online Tutorial: Introduction to Scientific I/O (HDF5)

HDF Workshops

Videos:

HDF5 is For Lovers
General Youtube search for hdf5  (many are regarding HDF5 software)