A- and A3 are actually two ratings from different ratings agencies: Standard & Poor's uses the A- rating, and Moody's uses the A3 rating. Both ratings indicate a relatively high level of creditworthiness.
At Moody's, the A3 rating comes after the Aaa, Aa1, Aa2, and Aa3 ratings. The A rating itself denotes that whatever securities are being rated are "upper-medium grade and are subject to low credit risk." The modifier 3 "indicates a ranking in the lower end of that generic category."
At Standard & Poor's, the A rating comes after the AAA and AA ratings, respectively. The A rating itself denotes a "strong capacity to meet financial commitments, but somewhat susceptible to adverse economic conditions and changes in circumstances." S&P can further modify the rating by adding a + or – to show the relative standing within the major rating categories.
Credit ratings attempt to measure the probability of default. Both the A- and A3 ratings are firmly in the "investment-grade" category, which means that they are among the safest obligations in the market.
When the ratings agencies change their ratings, the price of securities can change significantly. In some cases, the change in rating even dictates whether investors will have to buy or sell.
For example, many institutional investors (such as pension funds) are forbidden from investing in bonds rated below investment-grade. So if a bond is downgraded from A- to "junk" status, the fund manager would have to sell it. On the other hand, a fund manager of a junk bond ETF might want to buy it.