Tweed is a rough and course fabric that tends to be itchy. It is essentially unfinished wool. In general terms, tweed resembles cheviot or homespun but it is a bit more closely woven. In order to give the fabric a more lively look, different colored strands of wool (mainly subdued colors) are woven in a check or herringbone pattern.
Tweed is not a very modern fabric and is more commonly worn by older men in normal conditions (stereotypically known to be worn by college professors with elbow patches). It’s quite alright to wear this type of fabric to an outdoors event (tweed is moisture resistant and quite durable) – for example: heading to picnic, golf, country dance, etc… other than that, not a great wear for inside the city. This fabric is most commonly worn for hunting and shooting.
With all of this said, if you were to pick up a tweed jacket for fall outdoors-wear, you could pull off the look with a nice dark pair of jeans and a button down shirt. The jcrew picture in this article gives you an example of this.