Me gusta / a mí me gusta

[Tina]

I'm confused about when the 'a' is needed. Some examples in my book:

Me gusta el cine.
Me gusta tocar la guitarra.
No me gusta.

A mí me gustan los deportes.
A mí también. ¿Y a ti, Maria?
A mí no.

The book only says this:

The context may make it clear who you are referring to, but if it doesn't, you can be more specific by using the following construction with the preposition 'a' with exactly the same meaning as above.

I don't understand what this means. The context looks the same to me in both instances. The person is stating that they like something or they don't. Can someone help me understand?