Well, the wiki won't ever help you. You should go directly to the source; the TES:O website.
In any case:
Ebonheart Pact: the alliance was the result of the invasion of the Akaviri Kamal, who sacked Windhelm and then invaded Morrowind before being defeated at Red Mountain by the combined armies of Almalexia, Wulfharth, Vivec, and Jorunn Skald-king. They're invading Cyrodiil because they perceive Molag Bal as an existential threat to Nirn.
Daggerfall Covenant: Seems to be the result of a human endeavor to manufacture stability in the interests of trade and to ultimately revive the Empire in the wake of the chaos throughout Tamriel. They're invading Cyrodiil because the Aldmeri Dominion is, and want to prevent the Dominion from seizing White-Gold.
Aldmeri Dominion: According to older lore, the Dominion was formed after the Summerset Isles staged a coup in Valenwood (which was in chaos) and restored order by creating the Thalmor, a puppet governing body to rule over Valenwood. Although whether this is still true for this Dominion is unknown, since the events in question obstensibly took place after the events of TES:O. In any case, they're invading Cyrodiil now (according to TES:O) to end the chaos there and reclaim White-Gold (one of the mystical elven towers) as their own.