Processor
The processor of your laptop determines its speed and power.
A more powerful processor will make your laptop faster, more responsive and generally easier to use. More expensive processors, such as Core i7's, have more cores at their disposal, meaning they can do more work simultaneously without delay.
It's important to choose a processor that fits your needs. If you're doing video editing or gaming, a powerful processor with 4+ cores is almost a requirement.
However, for basic tasks like word document editing and browsing, a lower-end processor such as a Intel Pentium or AMD Athlon will probably suffice.