By changing to lighter strings you reduce the tension on the neck. The truss rod in your guitar is designed to counter the tension exerted by the strings. The strings bend it forward (in a concave arc like a smile). The truss rod bends the neck in the opposite direction - backwards (in a convex arc like a frown). Too much of a forward bend (smile) will cause the strings near the center of the fret-board to be too far away from the frets and hard to play. The truss rod is able to decrease the bow in the neck caused by the string tension.
With less string tension countering the action of the truss rod - it is able to cause the neck to bend towards a flat or convex curve (also known as a back-bow) in the neck. A flat neck or back-bow will cause fret buzz.
Ideally you will want a slight amount of relief in the curve of the neck and the action. You want the strings exerting more tension than the truss rod to give you a slight forward curve in the neck. So the string height in the center of the fretboard should be slightly higher off the fretboard than at either end.
You need a certain amount of relief between the strings and frets because when you pluck a string and cause it to vibrate, it does not vibrate only back and forth parallel to the fretboard. It vibrates all around in a circle. I call this oscillation. And like a jump rope, the oscillation will have a wider arc between the anchor points (on an open string the anchor points are the nut and saddle - fretted string = fret and saddle).
If you don't have enough room for the strings to oscillate (vibrate in a circle) they will contact the frets and that is what causes the buzz.
The image below came from an on line tutorial about adjusting your truss rod Guitarbitz tutorial on truss rod adjustment
Two things I recommend. 1) Adjust the truss rod to provide proper relief between strings and fret board with a slight smile curve. Refer to my answer in your question about saddle height Eva's Question on Saddle Height for a link to a good instructional resource for doing this yourself if you insist. Just be aware that making adjustments to your truss rod can cause damage to your guitar. Do not attempt to adjust your truss rod if you are the least bit unsure of what you’re doing. My recommendation is to take the guitar to a professional luthier or guitar technician for a complete set up.
The other thing you will want to do (#2) is to stretch your new strings in so they stay in tune. To stabilize your tuning, after all six strings have been brought to proper pitch, go back to the fattest (sixth string) and gently tug on it near the center of its length to "stretch" it. This will tighten up some of the slack where your string is wrapped around the tuning post and firmly seat the ball end in the bridge. You will notice after you do this that it is now out of tune (flat). Turn your tuning key to bring it back into tune. You can even go a tad sharp. Then repeat this process of gently tugging ("stretching" the string til it plays flat) and re-tuning until you can no longer make it play flat by tugging on it. Now the sixth string is nice and tight on the tuning post and will not be as inclined to go out of tune when you start playing.
Do the same thing for each subsequent string. Be especially careful on the skinnier strings not to tug too much or you could actually break the string. Gently tug just enough to make the string play flat.
It is important to get your guitar playing optimally as a beginner in order to maximize the reward of hearing your successful attempts to play the notes and chords you are learning. Buzzing strings can be just as frustrating as strings that are too difficult to press down. The good news is - your guitar is adjustable for a reason - and you (or your local guitar tech or friend who does their own set ups) will be able to get it playing the way it is designed to play.