I'm reading Talmud Bavli (the one from Koren) and I have a question concerning what I read in Shabbat Daf 12b. G-d is called the Omnipresent several times, implying to me that G-d is present everywhere. But then I read there also this: "Anyone who requests that his needs be met in the Aramaic language, the ministering angels do not attend to him to bring his prayers before God. ... A sick person is different. He does not need to bring his prayers before God because the Divine Presence is with him." This implies to me that the Divine Presence is only with a sick person and not with the other people who pray. But then, how should I understand the name "Omnipresent"? I apologize if this question is too basic, I only started to study these things recently.
Of course Hashem is everywhere. In some times and places, we perceive His presence more strongly. In those instances, we say that the Shechinah is present.
An analogy for this concept is radio waves. They're (pretty much) everywhere, but we can only "tune into" them when we have a receiver (i.e. a radio).
Sorry - I don't remember the source for this idea. I remember which one of my teachers said it, but not the source that he quoted.