The intent of the Alliance between Nazi Germany and Imperial Japan was to squeeze Russia, not Great Britain. Or rather "to squeeze the USSR".

But let's back up. First we should very quickly talk about how unlikely the alliance is, on the face of it. Relations between the two powers historically had been strained. Germany had strongly supported Russia during the Russo-Japanese war of 1904/5 (the Russians got curb-stomped). Germany had moved to support Russia during this fight because Japan had been spreading into China during the preceding decade, and the European colonial powers (Germany chiefly among them) felt that Japanese influence needed to be checked.

Japan had then joined World War One on the side of the Allies, not the Central Powers - on the face of it strange, but not really, because Japan wanted to snap up Germany's colonial possessions in the Pacific and (surprise surprise) China. Although the Allies were victorious, "white" countries like Australia and the Dutch opposed giving the Japanese all the Pacific territorial gains the Japanese believed they deserved, because those countries feared the increase in influence that would give over; coupled with that fear was anxiety about the detrimental effect an Asian imperial nation might have on the native people living in colonized countries (ie, it might make them 'restless'). This staunch opposition to what the Japanese felt was their rightful reward created a climate of Japanese resentment against all European parties involved in this dispute.

Couple this with the Nazi's rampant and ultimately suicidal levels of racism, you can understand why an Alliance between these two parties needed a pretty compelling reason to get off the ground.

That reason was the Soviet Union.

Hitler always wanted to expand towards Ukraine and western Russia; he spells it out, black and white in "Mein Kampf." ("Mein Kampf" is definitely the most boring book in the entire world, by the way, which perhaps explains why so few historians actually manage to read it.) The Soviet Union was a kind of loathsome pot-purri of everything the Nazis decided to hate - Slavs with prime land and communism.

But the Soviet Union was also awesome - huge in scale, ambitious in production goals (even if those goals weren't often reached), and their military was doctrinally advanced (the purges of the '30s caused chaos, but that's a different tale.) With the trans-Siberian railroad, and a Navy and an Army Group based at both ends (at least in theory), the Soviet Union was both a Pacific and a European power.

On the Japanese side, an Alliance with Hitler is probably going to prevent your old enemy the Soviet Union from taking advantage of the chaos to invade China. You would prefer your fragile puppet-states to remain intact while you take the fight to the Chinese interior; you can leave them reasonably thinly garrisoned so long as the Soviets are worried about being struck from behind if they move to invade them. So that explains that neatly.

But now you are racist Hitler. You know you will invade the Soviet Union from the west at some point. You don't really want the Eastern parts of it - Siberia and such. But there is someone who might want that East - an expansionist power with a proven military and an old grudge against the Russian state.

Hitler's calculation was that the alliance would tempt Japan to move North after invading China, working in cooperation with Germany to seize Siberia while the Germans invaded from the west; this would force the Russians to fight on two widely separated fronts. The transfer of men and arms to the western front would be impossible. All this, if only the Japanese turn their eyes north to the untapped oil fields of Siberia and not the infrastructure and vulnerability of the Dutch East Indies, to the south. The Soviet Union would probably have collapsed had this actually been done.

Well, the Japanese decided not to play. But you can see why the Alliance might have been so attractive to both parties at the time, even if it was ultimately a destructive arrangement.

EDIT: /u/Driftwood44, thank you for correcting my spelling/stupidity.

Both Nazi Germany and Imperial Japan were up and coming world powers which sought to break the influence of the old western powers, such as Britain and France, and expand at the expense of their neighbours - in Europe and the Pacific respectively.

Although Japan signed the Anti-Commintern Pact in 1936, they remained neutral with the USSR until 1945. Japan and Germany did had a common enemy in France. While the Germans invaded their western neighbours, the Japanese took over French Indochina. In the broadest sense, the alliance between Japan and Germany was simple convenience against common foes.

As a part of their compromise, Germany gave up it's claims to its old imperial possessions in the Pacific - such as Samoa and New Guinea. The Japanese aimed to establish an East Pacific Empire just as the Nazis wished to create lebensraum in eastern and central Europe.

Hitler was a little dismayed about the side lining of white people in places such as Australia and New Zealand, but saw this as for the greater good. Racially the Japanese were viewed favourably by the Nazis, particularly Heinrich Himmler, who was fascinated by Eastern spirituality, and were given the position of 'honorary Aryans'. According to Mein Kamf Hitler supported Japan in the early 20th century Russo Japanese war, due to his disdain for Slavs. However, Hitler later expressed concerns of Japanese expansion, and feared (if the Axis won WW2) that a showdown between the 'white' and 'yellow' races might one day occur.