A sextile in an astrological chart occurs when two planets are sixty degrees, or two signs, apart. Sextiles are considered a soft aspect -- one whose effects are comfortable and beneficial.
In fact, this aspect is such an easy one that you might not even notice its influence in your life; you might just think it's natural that you have such a smooth time in the particular area influenced by the two planets involved!
Sextiles bring opportunities, and what can seem like good luck -- but they won't necessarily make gifts fall effortlessly into your lap. You still have to focus your own energy on the area affected by the sextile to get the most benefits from the aspect.
For example, let's say that you have Mercury sextile Venus in your birth chart. The easy relationship between the planets of communication and love would result in a real facility with relationships, enabling you to talk with your lover in a sweet and open way and resolve arguments with ease -- or just avoid them in the first place.
But while you might think you're just lucky in love, in actuality, you're using that innate talent in a specific way; your natural diplomacy becomes a gift you give to your lover, and a tool you use in creating a successful relationship.
In general, sextiles encourage cooperation and make hard work feel easy. Even sextiles between the planets with more challenging energies make it easier to access those planets' good sides.
Here's an example of a sextile on a chartwheel: