An open a [a] we have in English in words like cut, unfair, mud. We produce this sound by opening the mouth, the chin goes downwards. The closed a, at least as far as the author sees it, doesn't exist in English. If you want to know how it sounds, just try to say cut without moving the chin, keeping your mouth closed. If you don't hear the difference, you will hear it if the two sounds are directly opposed.
[ɐ] [a] [ɐ] [a] [ɐ] [a] [ɐ] [a] [ɐ] [a]
If you want to start a career as a ventriloquist, this is the right moment. You can start with the closed a [ɐ].
The closed a is marked with an acento agudo in the case that it is not pronounced already as closed because of the general rules, see 3.4.1.
(The final -er in words like better is very similar to the closed a. It shouldn't therefore be a big problem to produce it.)
There is one situation where the difference between an open a and a closed a is really important. The first person plural presente of the verbs ending in -ar (falamos = we speak) is a closed a. (One could therefore write it as well falâmos, but since the accents is put on the penultimate syllable any way, there is no need to do that.) However the first person plural perfeito simples is pronounced with an open a and is written with a acento agudo.