The most important aspect of the monroe doctrine (1823) was that it

  showed the US backed the independence of Latin America.

Explanation:

The United States was still young at the time the Monroe Doctrine was declared, and did not have a powerful navy to be patrolling the South American coast at that time.  But the US did want to keep European powers from encroaching into the Western Hemisphere, and wanted to put Europe on notice to that effect.  

President James Monroe asserted the doctrine in his annual address to Congress in 1823.  The doctrine was that the US would not interfere in European affairs, but also would view any attempts by European powers to take control of any nation in the Western Hemisphere as a hostile act against the United States.

As reported by the US Office of the Historian, there were some additional motives in mind in the US position, in addition to backing the independence of Latin American nations.  "Monroe’s administration forewarned the imperial European powers against interfering in the affairs of the newly independent Latin American states or potential United States territories. While Americans generally objected to European colonies in the New World, they also desired to increase United States influence and trading ties throughout the region to their south."

the bar kochba rebellion (132-135) against the roman empire, also known as the second jewish-roman war, was the second major jewish revolt in judea and the last of the great jewish-roman wars.

after the first jewish-roman war of the years 66-73, the roman authorities took measures to crush any new attempt of rebellion in judea. his political situation was modified and instead of a prefect a governor of praetorian rank was appointed, and in the ruins of jerusalem the seat of a complete roman legion, the legio x fretensis was established.

the political and religious direction of the jewish people was left in the hands of the sanhedrin, with initial headquarters in yavne.

the direct causes of the rebellion vary according to the source. the roman historian dio cassius (155-229) attributes the revolt to the decision of hadrian to found in the place of jerusalem a roman city called aelia capitolina (aelia by its own name and capitolina in honor of the roman god jupiter). on the other hand, the jewish sources, while recognizing this resolution as true, assign higher priority to the decrees dictated by hadrian that forbade the brit milah (circumcision), the respect of the sabbath and the laws of purity in the family.

hadrian's intention was to "civilize" and incorporate the jews once and for all into the greco-roman culture. for greek and roman culture, circumcision was an intolerable mutilation.

the jewish tradition tells in the midrash tanjuma a meeting between rabbi akiva and the governor turnus rufus, where he asked for an explanation about the circumcision.

an additional legion, the legio vi ferrata, moved to the province to maintain order, and work began in the year 131 after the governor of judea, turnus rufus performed the founding ceremony of aelia capitolina. a roman coin with the inscription aelia capitolina was struck in the year 132.

the tannaim rabbi akiva, who without being named nasi directed the sanhedrin, convinced the other members to support the imminent rebellion.

the jewish leaders carefully planned the second rebellion to avoid the numerous errors that had been committed in the first one. in the year 132 the rebellion led by bar kochba quickly expanded from modiim throughout the country, defeating the x roman legion based in jerusalem and destroying the xxii roman legion that had come from egypt.