cpus are used to execute a sequence of stored instructions from a computer program, say microsoft word, and allows the information to be represented by the os and is important for pretty much everything you do. usually cpus fetch decode and execute instructions.
other examples of use are endcoding and decoding video, file compression, majority of the operating system functions etc
Not sure what you mean by the size of cpu do you the process it is built on, ie 45 nm, this is the size of the trasistors in that case the smaller the better, if you mean ghz faster is usually better but not always as cpu archietechture plays an important role and so does the use of multitple cores.
for example a dual core core 2 at 3.00 ghz is not going to be as good as quad core i7 clocked at 2.67 ghz (both are also different based on a different architecture), the higher clock speed doesnt always mean better performance
The alienware you mentioned has a 1.3 ghz cpu but it is dual core mean you can have two threads being processed at the same time (each core runs at 1.3 ghz, this DOES NOT mean that the speed overall is 2.6 ghz) this allow for better multi tasking and more instructions being processed at the same time
the alienware has a low powered cpu for battery life and i believe a switchable nivida gpu which means that you can turn it on for gaming and turn it off and used intergrated graphics for better battery life
a gpu is a graphics processing unit an is used mainly in graphically applications such as video games and is used to process he graphics you see on screen and is designed i different way from a cpu.
the cpu is relatively weak in the alienware but it is paired with a good gpu allowing games to be played but probably not always in their complete glory.
these funtions ive mention require both the cpu and the gpu to work when playing games for example the cpu is also used to calculate various things as well as the gpu and vice versa on word the gpu will display the screen whilst the cpu processes the input and so on
