Immortals are the Necrons' shock troops, deployed where regular Necron Warriors are insufficient. They used to be the soldiers of the Necrontyr Empire, and generally consented to the bio-transference process -- after all, an immortal living-metal body is a pretty big step up from a short-lived cancer-riddled sack of meat. While the soldiers were not nobles, they did have knowledge and experience that was valuable in the coming war with the Old Ones, so they were given bodies with better armor and superior weapons. They even retain some of their personalities, and are capable of some conversation, though it is basically limited to matters of battle and their voices are completely devoid of emotion (which is very annoying for the more hammy Lords who try to rile them up with inspiring speeches). They're a bit like the Cybermen from Doctor Who in some ways (which may not be a coincidence, given how prominent Doctor Who is in British popular culture). In the 7th edition codex, it is shown that Immortals do remember much of themselves, but thanks to their programming only feel rage and pride; a short story shows an Immortal taking the time to slowly crush a human skull for damaging his leg rather than quickly killing the offender.
They are veritable giants and big-as-a-Terminator huge, towering over even a Space Marine. If anything, bioconversion has allowed them to prosecute war with an even-greater efficiency. Unlike the Necron Warrior, who will fall back on defensive protocols should it be without orders, an Immortal will strive for victory using every tactic and strategy at its disposal if left to its own devices. An Immortal is incapable of adapting to new modes of warfare, but war has, even with technological advancements, remained the same across the eons, and an Immortal is seldom baffled in this manner.
For all that lore, the differences between Immortals and Warriors on the tabletop are that Immortals are slightly more expensive and get better weapons (gauss blasters or tesla carbines vs. gauss flayers or gauss reapers), one extra point of toughness, a better armor save (3+ vs. 4+) and one extra attack (with no melee weapon).
This is in contrast to 8th edition, where they only really had the extra armor and Tesla to differentiate themselves - the standard tactic then being to take large blobs of them, cast My Will Be Done which not only gave them great WS but also triggered the Tesla rule on 5's instead of just 6's.
In 9th edition, with Tesla still having garbage AP and now only triggering on unmodified 6's, Immortals are not looking quite as hot for damage dealing. This isn't helped by the fact that the Gauss Reaper that Warriors have been handed down has most of the features of the Gauss Blaster has (save for a few dynastic synergies). Their main upside is now instead that 10 Immortals, with their two attacks and extra toughness are much harder to bully off an objective (and still benefit from solid Resurrection Protocol.)