What it is:

Dilution is a reduction in proportional ownership caused when a company issues additional shares.

How it works/Example:

Let's assume you own 100,000 shares of XYZ Company. The company has 1,000,000 shares outstanding, meaning that you own 10% of the company. Shares of XYZ Company are trading at $5, so the company's current market value is $5,000,000 and your investment is worth $500,000.
XYZ Company wants to build a new plant, so it issues 500,000 shares. Your 100,000 shares are now only 6.67% of the company (100,000/1,500,000 = 6.67%). 
In the end, the dilution may be worth it if the plant makes XYZ Company more profitable. If however, the company issued those shares as part of an overly generous stock option program or to raise funds for projects that fail to contribute profit, the dilution may cause permanent damage to the value of your holding.

Why it Matters:

Dilution is the act of dividing the proverbial pie into ever smaller pieces, and it is usually not well received by investors. Several events can cause dilution, particularly secondary offerings, the conversion of convertible securities, option exercises, and warrant exercises. On occasion, companies purchase their own shares on the open market to combat dilution. It is important to note stock splits do not usually create dilution, because in a stock split the investor receives additional shares to preserve his or her percentage ownership and investment value.
Although dilution most noticeably affects ownership percentages, earnings per share calculations also consider the effects of dilution. This is why most public companies report both basic and diluted earnings, whereby potentially dilutive securities are treated as if they were already converted to outstanding shares. This effectively increases the number of shares over which the company's earnings would be spread if all potentially dilutive securities were exercised.
In some companies, shareholders can protect themselves from dilution if they have the right to purchase shares in any of the company's future stock issuances. These anti-dilution provisions, also called subscription rights or preemptive rights, usually appear in a corporation's charter.

Best execution refers to the imperative that a broker, market maker, or other agent acting on behalf of an investor is obligated to execute the investor's order in a way that is most advantageous to the investor rather than the agent.