Hi
Avenues are 6 lanes of traffic and are *usually* used for main thoroughfares through a city; many people will connect the entrance of the city to an avenue, then branch off to streets to build the rest of the traffic plan. Think of them as highways - I personally tend to use only a couple to make a way to get from one side of the city to another, or connecting the entrances if there are more than one.
For me, it works best to keep them fairly clear of buildings, and put crucial things like trade depots on a street directly connected to the avenue. Avenues are large (6 lanes of traffic instead of 4), and expensive; they can be difficult to manage. I have had success with streetcar avenues connecting one side of the city (residential and commercial) with the other side (industrial) to make a way for the sims to "commute", but it does take a lot of management. I had one city where I essentially made a "bypass" by elevating the avenue and running it from one entrance to the other and curving some streets off it like exit ramps. It looked cool, but it took a lot of work and I am just not talented enough to make the whole city work well enough with such a layout.
That's the fun of SimCity - trying different things to see how they work for you. I hope you can get the city you're striving for. Happy Building!