What does a capacitor “Series” signifies?
The series is the manufacturer's product family. The products in a series will have something in common, like a target application or package type, and will often share a datasheet. For example, if you select the Ceralam MR series on the Newark page, you'll find about 50 ceramic through-hole capacitors made by AVX. Here's the datasheet for the whole series. A series datasheet describes the whole product line. It should tell you how to construct a part number for a specific capacitor. Here's how the Ceralam MR datasheet does that:



The next several pages give the package dimensions for the different styles and list which capacitance values are available in each style. Finally, there's some mechanical information that's used in mass production systems.

For beginner/hobbyist purposes, I recommend ignoring the series. First, narrow down the results based on the main parameters (capacitance, voltage, etc.), then look at the package and size, then look at the price. If you still have a lot of options, pick whichever datasheet is your favorite. :-)

The best parameter to start with is actually package, on the far right. Since you're buying in small quantities, you only want things like cut tape, bulk, and tube packaging. Tape and reel is for when you want to buy thousands of units at once. This knocks out a lot of duplicate part numbers from your list.