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(These two images generated by "Where is M13?")
The Milky way Galaxy is a barred spiral, about 90,000 light years in diameter. The sun is located about 26,000 light years out from the center, one of about 200 Billion stars in the galaxy.
Here is another picture, showing the Sun buried in one of the spiral arms of the galaxy: the Orion arm. The Orion arm is now thought to be just a spur branching off from the "inner" edge of the larger Perseus arm (all remaining pictures are from The Atlas of the Universe):

As you can see in the above picture, the Sun is located relatively close to the inner edge of the Orion/Perseus spiral arm structure.
Zooming in on the vicinity of the Sun, here is a picture showing the Sun in relation to the nearby arms, along with notable stars and nebulae (the center of the galaxy is now below the picture):

This position, toward the inner edge of an arm, means that we are looking into the Orion arm when we are looking away from the center of the galaxy, and out of the arm (into the "space" between the Orion arm and the Sagittarius arm) when we are looking toward the center of the galaxy. There are actually as many stars in the "gaps" between arms as there are in the arms themselves, but the stars in the arms were formed more recently than the stars outside of the arms, and are generally much brighter.
Therefore, when we look toward the galactic center - in the direction of the constellation Sagittarius - we are looking away from the bulk of the Orion arm into a field of older, dimmer stars. On the other hand, when we look away from the galactic center - in the direction of the constellation Taurus - we are looking into the bulk of the Orion arm with all of its bright, newly minted stars. Since we only see the stars at night, that means that when the Sun is in Taurus (late March to late April), we see the stars in the opposite direction at night - that is, toward the constellation Sagittarius - a field of relatively dim stars. When the Sun is in Sagittarius (late November to late December), we see the stars in the direction of Taurus - a sector of the sky which is richly populated with bright stars. This is why the stars look brighter in the winter months than during the summer months - they actually are brighter stars.
Here's a picture of the celestial sphere, unfolded, with Sagittarius at the center, and the stars of Taurus at the extreme ends of both sides of the ellipse (folded up, these ends would be joined together to reconstitute the complete sphere).

Basically, the stars on the left side of this diagram are the stars we see during summer nights, and the stars on the right side of the diagram are the stars we see during winter nights. As you can see, there are far more bright stars on the right than on the left, when we are looking into, rather than away from, the Orion arm.
I highly recommend browsing through The Atlas of the Universe. The site allows one to zoom out to larger and larger scales, showing the local neighborhood of our galaxy: the Virgo Supercluster, of which our Milky Way galaxy is only one among some 50,000 galaxies, representing some 200 trillion stars. Continuing on, one can zoom out to see other superclusters in the neighborhood of our Virgo Supercluster - a neighborhood spanning several hundred billion light years, over 60 million galaxies, and containing over 250,000 trillion stars.
You can zoom out even further, but take a few deep breaths before you do, and make sure your feet are firmly planted on the ground, because the sheer enormity, magnitude, and elegance of the structure of the cosmos at the largest scales can make you feel pretty small and insignificant, and yet somehow proud to be part of it all.
My hat is off to Richard Powell, who has clearly put an enormous amount of care, work, and love into this site: one of the best science websites on the net.
Resources for exploring our galactic neighborhood:
The Atlas of the Universe - The web resource we've been using above.
Where is M13? - A nice tool for visualizing the various noteworthy objects in our galaxy.
Stellarium - A high quality planetarium program you can download for PCs or Macs - and, it's free!
Hayden Planetarium Digital Universe Atlas - A very powerful astronomical data visualization tool.


