The details of the reactions look like this:
CO2+H2O <> H2CO3
When CO2 dissolves in seawater, carbonic acid is produced via the reaction:
H2CO3 <> {H+] + HCO3
This carbonic acid dissociates in the water, releasing hydrogen ions and bicarbonate:
[H+]+[CO32-] <> [HCO3-]
[H+] represents a single positive H ion and so on
The increase in the hydrogen ion concentration causes an increase in acidity, since acidity is defined by the pH scale, where pH = -log [H+] (so as hydrogen increases, the pH decreases). This log scale means that for every unit decrease on the pH scale, the hydrogen ion concentration has increased 10-fold.

One result of the release of hydrogen ions is that they combine with any carbonate ions in the water to form bicarbonate:

This removes carbonate ions from the water, making it more difficult for organisms to form the CaCO3 they need for their shells.

The oceans are not, in fact, acidic, but slightly basic.

Acidity is measured using the pH scale, where 7.0 is defined as neutral, with higher levels called "basic" and lower levels called "acidic".

Historical global mean seawater values are approximately 8.16 on this scale, making them slightly basic.

To put this in perspective, pure water has a pH of 7.0 (neutral), whereas household bleach has a pH of 12 (highly basic) and battery acid has a pH of zero (highly acidic).

However, even a small change in pH may lead to large changes in ocean chemistry and ecosystem functioning. Over the past 300 million years, global mean ocean pH values have probably never been more than 0.6 units lower than today (6). Ocean ecosystems have thus evolved over time in a very stable pH environment, and it is unknown if they can adapt to such large and rapid changes.