Proposition 23 of Part V of the Ethics says:
The human mind cannot be absolutely destroyed along with the body, but something of it remains, which is eternal.
A demonstration is offered. The scholium to the proposition adds that 'we feel and experience that we are eternal'.
These views seem to form the apex of Spinoza's system, coming almost at the end of the Ethics as the apparent culmination of a long series of connected propositions. Although they are not particularly emphasised -- Spinoza left his readers to decide what mattered -- it would seem strange to imagine that they were not of importance to him.
To commentators, these views form the apex of his system in another way: as a pinnacle of difficulty, or a stumbling-block for the understanding. Some  have just give up on Spinoza at this point, believing that he had extended himself beyond any rational defence or explanation of his position, lapsing into paradox or mysticism. Others have avoided the real problems of interpretation with rhetoric. Even Pollock, normally so lucid, offers no better than this:
Spinoza's eternal life is not a continuance of existence but a manner of existence; something which can be realized here and now as much as at any other time or place; not a future reward of the soul's perfection but the soul's perfection itself. In which, it is almost needless to remind the reader, he agrees with the higher and nobler interpretation of almost all the religious systems of the world .
In addition to the general difficulty in seeing what Spinoza meant, and how it could be fitted into a general understanding of his thinking, there are at least two particular points where his opinion in Ethics V, 23
Understanding eternity has seemed to conflict with other important views that he expressed: where he has seemed inconsistent as well as, perhaps, unintelligible.
First, most readers of Part II of the Ethics have assumed that mind and body must exist together: 'The object of the idea constituting the human mind is the body - i.e. a definite mode of extension actually existing, and nothing else' , and so on. That view has often seemed (and often seems to students exasperated by Descartes) to resolve the paradoxes created by an immaterial spirit, affected by and affecting the extended body while retaining a capacity for immortality. Admittedly, although Spinoza may have evaded the problems of body-spirit dualism, he did land himself with the apparently awkward consequence that individual things, not just people, are 'animate, albeit in different degrees'  -- but otherwise, what he said in Part II of the Ethics about the constitution of people looked fairly sensible. So how could something of the mind 'remain' when the body was destroyed? That seems to be in direct conflict with the view that mind and body must go together.
Secondly, his thinking about time was elusive and never collected into a single coherent statement. He followed a conventional enough distinction between endless duration -- the experienced passage of time -- and timelessness or eternity . The eternal 'does not admit of "when" or "before" or "after" . A natural reading is that the eternal truths of geometry and philosophy will be timeless, with no 'before' or 'after', in contrast with human experience: eternity 'cannot be explicated through duration or time, even if duration be conceived as without beginning or end'.7 In the Demonstration to Ethics V, 23, we see that 'we do not assign duration to the mind except while the body endures'. Yet we are said to 'feel and experience' that we are eternal. Feeling and experiencing hardly sound relevant to the eternal truths of mathematics or philosophy. And even if they were, what we might call their human relevance would seem to be left as problematic. The type of eternity embodied or expressed by the eternal truth of the theorem of Pythagoras is hardly a type that might offer any consolation, hope or even interest to anybody except a Pythagorean. If eternity is distinguished from experienced duration, how could we experience eternity?
Maybe there is some religious interest in any philosopher who claims to demonstrate that part of the mind is eternal -- though, even more than with Spinoza's demonstrations for the existence of God, we are not thinking of proofs to convince the wavering or the unfaithful. It might be imagined that the eternity of the mind was of special personal significance, and that a demonstration of it was a central motive behind his work; but there is not a word of evidence for that view, and no hint of it in his letters or in his mature writings other than the Ethics.
As with his remarks about Jesus, these problems might seem to be incidental in terms of his narrowly philosophical interest to us. That is a view that he did something to encourage himself. As we have seen, his passage on eternity in Part V of the Ethics appears before two concluding propositions, which tell us that 'even if we did not know that our mind is eternal', the philosophical and moral conclusions of the remainder of the book would still hold. The overt reason for that conclusion is to underline that punishment and reward in an after-life have no part to play in moral philosophy -- deep scorn is poured over such an idea -- but it does not take a great deal of suspiciousness to say that Spinoza may also have been hedging his conclusions on eternity with a proviso that they were logically optional to his other views. So, philosophically, it might not look too harmful to disregard them.