In this week's parshah we see that Yaakov was very concerned about leaving Eretz Yisroel. Hashem appears to him and tells him not to worry. He Himself would go down to Egypt with him, and would return the Jewish people to Eretz Yisroel at the proper time. Hashem's gdescending into galus is with klal yisroel is known as "galus haschechina".
This concept of "galus hachechina" has been understood in the classic literature on several different levels:
Firstly, the Torah tells us that when someone kills accidentally, he must run away to stay in one of "the cities of refuge". But it is not necessary that he suffer there. Quite the contrary. The Torah says, "he should live there" (until the death of the high priest.) The connotation of that phrase is that the murderer should have a pleasant stay there. It is for this reason that the rabbis of the Talmud commented that if the murderer is one who enjoys learning Torah, we must provide him with a shiur. His rabbi must also visit the "city of refuge" to present Torah lectures for the enjoyment of the murderer. The punishment of going into galus is bad enough, and should not be made worse by having him miss his regular Torah studies.
Similarly, when Hashem punishes the Jewish people and sends them into galus He personally accompanies us into that galus so that we will not suffer more than is necessary, and so that our stay will not be too terrible.
Secondly, the Talmud recalls instances when the rabbis had to place a cherem on a Torah scholar (for having violated sins), and would simultaneously put themselves into cherem. This was in order to remind themselves to be "mattir" the cherem on the Talmid Chochom at the same time they would be "mattir" their own cherem.
So too, Hakadosh Baruch Hu goes into galus along with us, "suffering along with Am Yisroel" so to speak. He will certainly not be able to forget about redeeming us from galus, since He will need to redeem Himself from the galus.
In the Tanya, Kabbalistic sources are quoted where a totally different understanding of the term (galus hasheschina) is presented. When Hashem created the entire world ex nihilo, the basic and fundamental nature of all things was nothingness; that nothing else existed (outside of Him). Even when everything in the world was brought into existence, if not for the continuos will of G-d that all these things continue to exist, everything would revert to the state of non-existence. (Ramban on Parshas Bereishis understands that this is the meaning of the phrase which is oft repeated, "G-d saw that everything was good", i.e. He willed that everything should continue to exist). This continued will of G-d is referred to as "sparks of sanctity" (nitzotzos of kedusha). These "sparks of sanctity" preserve all things that continue to exist in the world - holy (people and objects), secular, and profane alike. In this sense there is a galus hashechina, because these "sparks of holiness" are "arrested" (so to speak) in unholy things, places, and people. One can truly refer to this state as one of "melech assur borehotim" (as if the King is imprisoned). Everything in the world yearns (so to speak) to have a meaningful existence. This will only came about if and when each created item will serve to heighten the glory of Hashem; i.e., if it will be used in the performance of some mitzvah or another. This is the symbolic meaning of the Talmudic comment as to what positive result was accomplished by sending the Jews into galus? Many non-Jews converted to Judaism, i.e., more of the secular world became involved in the observance of mitzvos, and had thereby attained a meaningful existence.