Its Meaning: It is to seek support, aid, in a time of distress, hardship, and it is connected to Ruboobiyyah, and it is worship.
Its Conditions: That the one from whom Istigaathah is sought is:
a) Hayy (living)
b) Haadir (present in the same location)
c) Samee' (hearing)
d) Qaadir (able)
These conditions relate to mankind.
And as for Allaah He is Ever-living, and is present in the sense that nothing escapes his knowledge, will, hearing, sight, and command (while He is above the Throne, above the seven heavens), and he is all-hearing, and he is all-powerful and able, and to him belongs Ruboobiyyah. Thus, Istigaathah and providing aid and relief and support belongs to Him alone.
As for humans, then they do not possess these qualities absolutely, at all times, in all situations, thus, they die, they are not present, they do not have power or ability over many things (outside of their control), and they cannot hear those in distress because their hearing is limited. Thus, the combination of these conditions are required for Istigaathah through mankind, so that it does not enter into the Major Shirk.
When any of the four conditions are not present it is Major Shirk.
Seeking Istigaathah from a dead person.
Seeking Istigaathah from a person who is remote, distant from you, even though he is alive, hears and is able (in what you seek from him).
Seeking Istigaathah from a person who cannot hear you (like one who is dead, or far away in a different place), even though he is able (in what you seek from him).
Seeking Istigaathah from a person who is not able in that which you are seeking istigaathah (like asking someone to remove your illness or pain or calamity, or to calm the violent ocean, and so on, from those things that mankind have no control over, but only Allaah has control over), even if he is living, present and hears you.
Thus, the scholars have specified conditions for making Istigaathah from other than Allaah, for it not to be considered Shirk, and they are that the one being sought for aid, is living, present, hearing, able.
Further Clarifications: You fall into a lake, and you are holding onto some debris, near the shore. So you firstly seek aid from Allaah, seeking Istighaathah through him, depending upon him, then you shout hoping that someone might hear you. This is not major Shirk. Because you are shouting to bring the attention of one who is alive, present in that area, can hear, and is able to pull you out by any of a number of methods. So your call is to the creation in that which they can actually help you, should any one of them be present in that area. However, you acknowledge that it is Allaah who is actually helping you, should help arrive, and that He is called upon first, and heart depends upon Him, and that by shouting to bring the attention of someone is from the ways and means that are permitted legislatively in the likes of this situation, in order to receive His support and aid. Apply this to all other similar situations.
You fall into a lake, and you are holding onto some debris, near the shore. So you shout, "O Abdul-Qadir al-Jeelaanee". This is Major Shirk. Or you shout, "O Fulaan", for a friend who is alive, hearing, able, that you know is certainly not in that area but miles away, or hundreds of miles away, at home, and cannot hear you or help you, but you call upon him in expectation of a response. This is Major Shirk.
So the issue revolves around the presence of these conditions and their absence.
Source: Adapted from Sharh Thalaathat Usool of Shaykh Saalih Aal ash-Shaykh, with some additional points and explanations added.
May Allaah establish our hearts upon Tawheed and make us remain upon that in every instance of our lives. Ameen.