There is an amazing answer on mathematics stackexchange which defines what a self-financing strategy is—both in the discrete and continuous sense. Please check out this short answer to better understand my question.
I have a short follow-up question: Baxter and Rennie—while defining a self-financing strategy—requires the portfolio process to be previsible. The way the answer in the link arrives at the definition of self-financing, which is also the way I derive it, doesn't seem to require previsiblilty.
We are holding $(\Delta_t, E_t)$ over $t$ to $t+1$, which will be know to us at time $t$, even if the process is just adapted; previsiblilty is not required to know $(\Delta_t, E_t)$ at time $t$.
Extra for those who are interested: As always, things get muddier in the continuous time setting.
I think I have an intuition for what previsibility means when dealing with continuous processes: if a process $\phi$ is left-continuous, then we can know it's value $\phi(t)$ at a particular time $t$ with arbitrary precision by pushing the inputs close enough to $t$ from below, without actually having to reach $t$; this makes the value of $\phi(t)$ predictable with information upto but not including time $t$.
But it isn't clear to me why this previsibility is required while arriving at a sensible definition of a self-financing strategy —as the answer in the link succeeds to do.