This article expands on a post on Twitter by Professor Karol Sikora an oncologist. The article he is referring to is this one in the Journal Cell.

The paper talks about T cells in our blood which are part of our immune response. We don’t readily know about how may we have of these but we do know about antibodies for Covid-19 and we can now test for these. If you have antibodies for Covid-19 you will have specific T cells.
There are two main types of T cells of interest here CD4 and CD8. CD4 T cells target daily invaders, they are workhorses.

CD8 T cell target cancer and specific diseases, such as Covid-19.

If you lose CD4 T cells or they drop in number you can get ill for lots of reasons. (HIV patients have low CD4 counts).
The paper shows the levels of CD4 and CD8 cell after recovery from Covid-19. 

In the diagram we can concentrate on the CD4 and CD8 percentages the other items are additional immune components.

CD4 and CD8 T cell count in patients exposed and unexposed to Covid-19 from Cell Pre Proof paper

No surprise then that Covid-19 patients have both, a full complement of CD4 T cells 100% and a 70% complement of CD8 T cells, but  what comes next is unexpected,  in a quote from the paper, “While spike− and non-spike−specific CD4+ T cell responses were detectable in all COVID-19 cases, cells were also detected in unexposed individuals. These responses were statistically significant for non-spike-specific CD4+ T cell reactivity.

What we are saying is that there is already a number of T-cells needed to fight Covid-19, even in unexposed patients. From the diagram 50% of CD4 T-cells with even 20% of the more specialised CD8 T cells.
These must have come from previous exposure to coronaviruses, though a different type of coronavirus. They can’t have come from Covid-19 infection because the samples came from blood extracted between 2015 – 2018 i.e. pre the Covid-19 virus.
So in summary this means that there is a proportion of the population that already have a pre-prepared immune system to tackle Covid-19. Not full blooded immunity with antibodies but still an ability to stop the virus nonetheless.