I am attaching two books here where you can find all standard representations of Bessel functions with adequate interpretation. Both books are considered standard references, one of which is by NIST! Better save them in your hard drive. 

For worked out examples, the book by Bowman (third attachment) will be more than enough.

Bessel functions are often encountered in modelling of wave propagation in fluids, waveguides etc. You can find such information in respective Mathematical Physics books (Arfken, Kreyszig, Stroud etc).

65 MB in total, I guess.

Hope it helps!

3 more books:

1. An old classic by Watson - Theory of Bessel functions

2. Another classic by Gray & Mathews - A treatise on Bessel functions and their applications to physics

3.  Korenev - Bessel functions and their applications (2002)

I think that you need to understand where Bessel functions come from. Here you can read quickly the basics: https://en.wikipedia.org/wiki/Bessel_function

First the differential equation to which Bessel function is a solution is given in the text. Still not very intuitive. Next you can see that "Bessel functions for integer α are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer α are obtained when the Helmholtz equation is solved in spherical coordinates... Bessel functions are therefore especially important for many problems of wave propagation and static potentials".  You can also see the plot of those functions: they behave like sine wave with declining amplitude. Spherical Bessel function with index 0 also behaves as Sin(x)/x, further functions include more rapidly vanishing functions at infinity. It is useful to use asymptotic series for them.

Examples of application are also given there. They include applications from different branches of physics: 

- Electromagnetic waves in a cylindrical waveguide

- Pressure amplitudes of inviscid rotational flows

- Heat conduction in a cylindrical object, etc.

Quantum Mechanics on the Macintosh

Siegmund Brandt, Hans Dieter Dahmen

Springer 1991 and/or Springer 1995

There is a large section about special functions with many examples and exercises

I would recommend Bowman's book as well (Dover printed a cheap edition if you want a printed copy).

Thank you everyone for your valuable time and reply. All the information helped me enormously.