The first two divisions of Poland (in the 12th century, and in the 18th century) occurred primarily because of the severe weakness of central royal authority. Even by the standards of the 12th century, Poland was highly decentralised, with vast amounts of power and autonomy granted to regional noblemen and barons. This continued to get worse over the years until eventually all semblance of royal authority disappeared and Poland was fractured into a dozen or so minor principalities, each ruled by a different lord. Some may have continued to pay lip-service to the Polish king as their overlord, but in practice they were independent rulers. The Mongol invasions of the mid-13th century also disrupted any attempts at reasserting central authority. This type of political situation was not uncommon in the medieval era, as a similar state of affairs existed in both Germany and France following the division of the Carolingian Empire (848); Poland, however, managed to reunite its disparate provinces and reassert some semblance of central royal authority relatively more quickly than either of these other two regions did, and by the early 14th century Poland could reasonably be considered a unified country once again.
As for the more well-known partition of the Polish-Lithuanian Commonwealth in the 18th century, it occurred partially because of the same reasons above, although some more elaboration is required. Poland's political setup was somewhat unique, in that while there was still a king, he was elected by the Sejm, a legislative body consisting of a few hundred noblemen and aristocrats of varying social rank (e.g. some were powerful and wealthy barons, while others were mere knights). It could be seen as roughly comparable to the British House of Lords in the same era, although the Polish Sejm had considerably more power, to the degree that it was often them that dictated Polish-Lithuanian policy, and not the king. The nature of Polish-Lithuanian kingship wasn't just elective, but also foreign; throughout the 16th to 18th centuries, almost every king of Poland-Lithuania was foreign-born, with kings hailing from countries such as France, Sweden and Saxony. This inevitably led to some of these kings attempting to re-orientate Polish foreign policy to service the goals of their original home country (similar to what King George I of Great Britain did with his native Hanover). This frequently led to major disputes with the Sejm, who attempted to block any foreign-focused initiatives and further restrict the king's authority. By the early 18th century the king was little more than a rubber stamp for the Sejm's legislation.
Arguably the single greatest flaw of the Polish-Lithuanian government was the veto function in the Sejm; amazingly, if even only one single member of the Sejm decided to veto a piece of legislation, it would be blocked and not carried out. As one can imagine, this led to a virtual paralysis in Polish-Lithuanian governance, as many members of the Sejm instantly vetoed any legislation that even appeared to be attempting to limit the excessive power and influence of the nobility in favour the central government. Poland had no Louis XIV to force the nobility to bend to his will; the kings were often powerless to stop the continued dominance on the barons in the Sejm, who were interested solely in strengthening and expanding their own wealth and estates, even to the detriment of the Polish state. Even during several wars, the king could raise no more than a few thousand men and had to rely on his barons, but fearing that giving the king more soldiers would risk him becoming emboldened, they often just refused to help, even as their country was being invaded.
Added onto these already considerable domestic political problems were larger geopolitical ones. The Polish-Lithuanian Commonwealth (PLC) was the largest unified country in all of Europe proper (excluding the Ottomans and Russians) between the 16th and 18th centuries, and they had much military success against a variety of enemies on all sides (culminating in the Great Turkish War of 1683-99), but by the beginning of the 18th century things were starting to change to their detriment. The country had been absolutely devastated and laid waste to by the Swedish armies under King Charles XII during the Great Northern War, and its king overthrown. This led to a power vacuum which was eventually filled by the Russians; Peter the Great installed a Russian puppet king and ensured the PLC towed the line and supported Russian foreign policy, and allowed Russian armies unlimited access through the country. The crushing defeat of Sweden meant that Russia was now the undisputed master of Northern and Eastern Europe; their economy was stronger, their army larger, and their political leadership more unified and absolute. For half a century the PLC was little more than a client state of Russia's.
The three partitions of the PLC between the 1770s and 1790s was thus enabled entirely because of the weakness and paralysis of the Polish state, and its unfortunate geographic location of being surrounded by three European Great Powers - Russia to the east, Prussia to the north-west, and Austria to the south-west. Even against only one of these powers the PLC would not have been successful, and when a myriad of political and strategic factors combined to initiate the partitions (a whole other topic in itself), they were almost helpless to defend against it. Only before the third and final partition in 1795 did the Sejm finally realise they were the problem, and they granted the king (ironically the former lover of Catherine the Great of Russia, and the puppet she installed on the Polish throne years ago) more power and authority, outlined in a US-style constitution, in an attempt to rally support against the foreign invaders, but it was too little and too late.
The final partition, in 1939, was a relatively more straight-forward affair; there wasn't nearly as much internal political division, but rather the simple reality that Poland's military was not large enough to defend against the two strongest powers on the continent invading at once. Against one of them only, they might have stood a chance (I'm no WWII expert, so I can't say for sure) but against both it was simply impossible.
Source: Poland by Adam Zamoyski