How is a carboxylic acid acidic?
There is a lot in chemistry that cannot simply be explained by Lewis structures, usually requiring a detailed molecular orbital description to rationalise observations.

For example considering a carboxyl group versus a simple hydroxy group. The carboxyl group has a $\mathrm{p}K_\mathrm{a}$ of approximately $5$ while the hydroxy group has a $\mathrm{p}K_\mathrm{a}$ of approximately $15$. In Lewis structures, these two look identical save the neighbouring carbonyl group.

Why can this hydrogen be abstracted easily at all? The hydrogen on a neighbouring carbon (e.g. $\ce{C\mathbf{H}3COOH}$) is not easily abstracted ($\mathrm{p}K_\mathrm{a} \approx 25$ if I recall correctly). The Lewis structure in itself provides no information. You need to additionally consider the concept of polar bonds to explain it: The $\ce{O-H}$ bond is polarised towards oxygen, that means the hydrogen already feels as if it were somewhat like a $\ce{H+}$ and therefore the transition to the true $\ce{H+}$ is easier.

While that explains the acidity per se, it doesn’t explain why one is more acidic than the other. The theory says, that an acid is stronger if its conjugate base is more stable. Since we cannot rationalise the different acidities from looking at the acids, let’s look at the conjugate bases. In one, we just generate an alcoholate much like a hydroxide ($\ce{R-O-}$). Nothing special-looking. The same for a carboxylic acid. No distinction. (However, this clearly shows why $\ce{C-H}$ bonds are usually not acidic: the carbanion is very unstable when compared to an oxyanion.)

Since we cannot find the origin of acidity, we need to expand our theory. Specifically, this is where resonance comes into play as a partial representation of some features of molecular orbital theory in Lewis structures. The carboxylate can resonate between two different structures as shown in the scheme below. Therefore, every oxygen atom only has to take the burden or half a negative charge ($\ce{O^{\frac{1}{2}-}}$). This is much more stable than having a full negative charge — even for an electronegative element such as oxygen. The third structure of the scheme simply displays a way of drawing ‘something in-between’: Both bonds are somewhere between a single and a double one and the charge is located on both atoms simultaneously (but that is not easily drawn with chemical drawing programs).