The choice of radicals (部首{ぶしゅ}) as in the dictionary radicals (as opposed to any other selection of components), comes from Chinese and presumably was adopted alongside the kanji themselves.
The first source to use radicals was a second-century Chinese dictionary called Shuōwén Jiězì (說文解字 - in Japanese 説文解字{せつもんかいじ}). This included 540 radicals. The set of 214 radicals popularly used today are often called Kangxi radicals from the name of a standard Chinese dictionary of the 18th century which used them (but they were used in earlier works). There is more discussion on the Kangxi radicals in an earlier question here. The Kangxi radicals are generally used to be consistent, but there could be lots of ways of splitting up the characters. Simplified Chinese uses a set of 187 radicals (Xinhua Zidian radicals), for example.
The point of the radicals was never to tell you what the meaning of a character was, but to simply provide a way of indexing. Using a paper dictionary, if the characters are indexed by radical rather than sound it is possible to look up characters you don't know the reading of (even if you have to check a couple of possibilities). When using a physical dictionary, that's quite useful and saves time.
With computers there are other methods to find kanji, even when you can't copy-paste or don't know the reading (multi-radical/component search, handwriting input), so knowing what the dictionary radical is becomes less important.
There are still many cases where there are obvious patterns, and these can help particularly when remembering how to write a kanji. e.g. 金 on left hand side is normally related to metal in some way - names of metals or things made out of metals - 金、銀、鉛、鈴、銅、鍵、etc.
Many body parts have 月 in (in these kanji this radical was 肉 originally and is sometimes called 肉月), as can be seen in 肺、臓、胆、肝、脚、胴, etc, and I believe in this case it's pretty much always on the left hand side.
Or how about 犭? Actual beasts (猪・狼・猿・猫), kanji with a connection to hunting (狩, 猟、 狙, 獲 ), and kanji that you can connect metaphorically to beasts (犯 and 猛, for example), all feature.
You don't have to know the names of all the radicals or what they originally "meant" (in many cases the exact origin of a kanji is not 100% clear anyway), but being aware of common components can provide a sort of memory hook for those cases where there's some sort of connection between the components and either the meaning or reading of the kanji.
