For example, today there was India v Australia and India A vs New Zealand A. What does the extra A mean after the team?
Teams belonging to a given association (such as a country, region, or club) are usually ranked according to which is "best".
This ranking is almost invariably labeled under one of two ways:
the best team is the A team, the second-best team is the B team, and so on along the alphabet. Countries tend to adjust this pattern by giving a special name to their highest-ranked team and shifting the regular names down the order.
the best team is the first or 1st team, the second-best team is the second or 2nd team, and so on along the ordinals. This labeling is often followed by the number of on-field players in the game, in word or in Roman numerals, so that a top cricket or football team is the First Eleven or 1st XI; a top rugby team is the First Fifteen or 1st XV.
Other methods are to select a given category with a series of nouns in a known order, and apply these names to the ranking.
To quote the wiki page
The list was the work of Philip Bailey and the name is derived simply from there being a list A and a list B. link
And the term relates to this a team representing the country in a List A match that is not the main international team.
The term came to prominence during the 1994–95 Benson and Hedges World Series Cup in Australia when the Australia A team was added to the international Triangular series as Zimbabwe was seen as not competitive enough to have the standard 3 teams in the tournament.
The Australia A side featured many future stars Ponting,Hayden,Blewett, Martyn and ended up meeting the Australia side in the final. The Australia side went on to win the final series but controversially they added Paceman Paul Reiffel to their squad who had been dominating for Australia A then made him twelfth man for the Australia team so they didn't have to face him.